×

Santini, Paolo Maria

Author ID: santini.paolo-maria Recent zbMATH articles by "Santini, Paolo Maria"
Published as: Santini, P. M.; Santini, Paolo; Santini, P.; Santini, Paolo Maria; Santini, Paolo M.; Santíni, Paolo Maria

Publications by Year

Citations contained in zbMATH Open

101 Publications have been cited 1,249 times in 795 Documents Cited by Year
Integrable symplectic maps. Zbl 0734.58023
Bruschi, M.; Ragnisco, O.; Santini, P. M.; Tu, Guizhang
75
1991
Dromions and a boundary value problem for the Davey-Stewartson 1 equation. Zbl 0707.35144
Fokas, A. S.; Santini, P. M.
73
1990
Recursion operators and bi-Hamiltonian structures in multidimensions. I. Zbl 0674.35074
Santini, P. M.; Fokas, A. S.
67
1988
Recursion operators and bi-Hamiltonian structures in multidimensions. II. Zbl 0706.35129
Fokas, A. S.; Santini, P. M.
67
1988
An elementary geometric characterization of the integrable motions of a curve. Zbl 0941.37532
Doliwa, A.; Santini, P. M.
65
1994
Multidimensional quadrilateral lattices are integrable. Zbl 1044.37528
Doliwa, Adam; Santini, Paolo Maria
65
1997
Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation. Zbl 1236.37042
Manakov, S. V.; Santini, P. M.
40
2006
Transformations of quadrilateral lattices. Zbl 0987.37070
Doliwa, Adam; Santini, Paolo Maria; Mañas, Manuel
38
2000
Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy. Zbl 0827.58024
Doliwa, Adam; Santini, Paolo Maria
34
1995
The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices. Zbl 0969.37528
Cieśliński, Jan; Doliwa, Adam; Santini, Paolo Maria
30
1997
The recursion operator of the Kadomtsev-Petviashvili equation and the squared eigenfunctions of the Schrödinger operator. Zbl 0613.35073
Fokas, A. S.; Santini, P. M.
30
1986
Darboux transformations for multidimensional quadrilateral lattices. I. Zbl 1006.37501
Mañas, Manuel; Doliwa, Adam; Santini, Paolo Maria
29
1997
On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking. Zbl 1136.35083
Manakov, S. V.; Santini, P. M.
25
2008
A hierarchy of integrable partial differential equations in \(2+1\) dimensions associated with one-parameter families of one-dimensional vector fields. Zbl 1131.37061
Manakov, S. V.; Santini, P. M.
23
2007
Integrable three-dimensional lattices. Zbl 0481.35046
Levi, D.; Pilloni, L.; Santini, P. M.
22
1981
The direct linearization of a class of nonlinear evolution equations. Zbl 0557.35111
Santini, P. M.; Ablowitz, M. J.; Fokas, A. S.
22
1984
\(\bar \partial\)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice. Zbl 0908.35125
Doliwa, A.; Manakov, S. V.; Santini, P. M.
21
1998
On the limit from the intermediate long wave equation to the Benjamin-Ono equation. Zbl 0543.45008
Santini, P. M.; Ablowitz, M. J.; Fokas, A. S.
21
1984
LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes. Zbl 1425.94046
Baldi, Marco; Barenghi, Alessandro; Chiaraluce, Franco; Pelosi, Gerardo; Santini, Paolo
21
2018
The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice. Zbl 0997.37052
Doliwa, Adam; Santíni, Paolo Maria
20
2000
On the solutions of the second heavenly and Pavlov equations. Zbl 1184.35279
Manakov, S. V.; Santini, P. M.
20
2009
The transition from regular to irregular motions, explained as travel on Riemann surfaces. Zbl 1157.70309
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
17
2005
On the dispersionless Kadomtsev-Petviashvili equation in \(n+1\) dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking. Zbl 1241.35181
Manakov, S. V.; Santini, P. M.
16
2011
Multiple-scale perturbation beyond the nonlinear Schrödinger equation. I. Zbl 0890.35139
Degasperis, A.; Manakov, S. V.; Santini, P. M.
16
1997
Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction. Zbl 0962.35510
Mañas, Manuel; Santini, Paolo Maria
15
1997
The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes. Zbl 1383.35210
Grinevich, P. G.; Santini, P. M.
15
2018
LESS is more: code-based signatures without syndromes. Zbl 1504.94204
Biasse, Jean-François; Micheli, Giacomo; Persichetti, Edoardo; Santini, Paolo
15
2020
Bi-Hamiltonian formulation of the Kadomtsev-Petviashvili and Benjamin-Ono equations. Zbl 0695.35184
Fokas, A. S.; Santini, P. M.
14
1988
Energy exchange of interacting coherent structures in multidimensions. Zbl 0696.35180
Santini, P. M.
14
1990
Nonlocal integrable partners to generalized MKdV and two-dimensional Toda lattice equation in the formalism of a dressing method with quantized spectral parameter. Zbl 0739.35090
Degasperis, A.; Lebedev, D.; Olshanetskii, M.; Pakulyak, S.; Perelomov, A.; Santini, P.
13
1991
Integrable lattices and their sublattices: from the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme. Zbl 1121.37058
Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.
13
2007
Charged free fermions, vertex operators and the classical theory of conjugate nets. Zbl 1041.81058
Doliwa, Adam; Mañas, Manuel; Martínez Alonso, Luis; Medina, Elena; Santini, Paolo Maria
12
1999
A unified algebraic approach to integral and discrete evolution equations. Zbl 0725.45005
Ragnisco, O.; Santini, P. M.
12
1990
Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals. Zbl 1126.37040
Grinevich, P. G.; Santini, P. M.
12
2007
The periodic Cauchy problem for PT-symmetric NLS. I: The first appearance of rogue waves, regular behavior or blow up at finite times. Zbl 1411.35244
Santini, P. M.
12
2018
The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes. Zbl 1454.35340
Grinevich, P. G.; Santini, P. M.
11
2019
A reaction attack against cryptosystems based on LRPC codes. Zbl 1453.94112
Samardjiska, Simona; Santini, Paolo; Persichetti, Edoardo; Banegas, Gustavo
9
2019
The dispersionless 2D Toda equation: Dressing, Cauchy problem, longtime behaviour, implicit solutions and wave breaking. Zbl 1165.37039
Manakov, S. V.; Santini, P. M.
9
2009
LESS-FM: fine-tuning signatures from the code equivalence problem. Zbl 1485.94128
Barenghi, Alessandro; Biasse, Jean-François; Persichetti, Edoardo; Santini, Paolo
9
2021
Wave breaking in solutions of the dispersionless Kadomtsev-Petviashvili equation at a finite time. Zbl 1352.35148
Manakov, S. V.; Santini, P. M.
9
2012
Nonlinear evolution equations associated with a Riemann-Hilbert scattering problem. Zbl 0581.35075
Degasperis, A.; Santini, P. M.; Ablowitz, M. J.
8
1985
Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking. Zbl 1226.35064
Manakov, S. V.; Santini, P. M.
8
2011
The general solution of the matrix equation \(w_t + \sum^n_{k=1} w_{x_k}\rho^{(k)}(w) = \rho (w) + [w, T \tilde{\rho}(w)]\). Zbl 1209.15022
Santini, P. M.; Zenchuk, A. I.
8
2007
Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter. Zbl 0761.35094
Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P. M.
7
1992
Asymptotic lattices and their integrable reductions. I: The Bianchi-Ernst and the Fubini-Ragazzi lattices. Zbl 1001.37073
Doliwa, A.; Nieszporski, M.; Santini, P. M.
7
2001
Numerical instability of the Akhmediev breather and a finite-gap model of it. Zbl 1477.37081
Grinevich, P. G.; Santini, P. M.
7
2018
Integrable nonlinear evolution equations with constraints: I. Zbl 0762.35104
Santini, P. M.
6
1992
Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case. Zbl 1408.35172
Grinevich, P. G.; Santini, P. M.
6
2018
Dressing method based on the homogeneous Fredholm equation: quasilinear PDEs in multidimensions. Zbl 1123.35074
Zenchuk, A. I.; Santini, P. M.
6
2007
The linear and nonlinear instability of the Akhmediev breather. Zbl 1477.35240
Grinevich, P. G.; Santini, P. M.
6
2021
Cryptanalysis of LEDAcrypt. Zbl 1504.94093
Apon, Daniel; Perlner, Ray; Robinson, Angela; Santini, Paolo
6
2020
The Cauchy problem for the Pavlov equation. Zbl 1332.35324
Grinevich, P. G.; Santini, P. M.; Wu, D.
6
2015
Cellular automata in \(1+1\), \(2+1\) and \(3+1\) dimensions, constants of motion and coherent structures. Zbl 0809.58021
Bruschi, M.; Santini, P. M.
5
1994
Geometry of discrete curves and lattices and integrable difference equations. Zbl 0935.53002
Doliwa, Adam; Santini, Paolo Maria
5
1999
The remarkable relations among PDEs integrable by the inverse spectral transform method, by the method of characteristics and by the Hopf-Cole transformation. Zbl 1140.37020
Zenchuk, A. I.; Santini, P. M.
5
2008
The inverse spectral transform for the Dunajski hierarchy and some of its reductions: I. Cauchy problem and longtime behavior of solutions. Zbl 1331.35313
Yi, G.; Santini, P. M.
5
2015
Partially integrable systems in multi-dimensions by a variant of the dressing method. I. Zbl 1122.37053
Zenchuk, A. I.; Santini, P. M.
4
2006
Nonlocality and the inverse scattering transform for the Pavlov equation. Zbl 1344.35126
Grinevich, P. G.; Santini, P. M.
4
2016
Integrable lattices and their sublattices. II: From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices. Zbl 1152.81403
Doliwa, A.; Nieszporski, M.; Santini, P. M.
4
2007
Geometry of Winter model. Zbl 1356.81163
Aglietti, U. G.; Santini, P. M.
4
2015
Integrable and nonintegrable initial boundary value problems for soliton equations. Zbl 1362.35249
Degasperis, A.; Manakov, S. V.; Santini, P. M.
4
2005
Geometric discretization of the Bianchi system. Zbl 1087.53020
Doliwa, A.; Nieszporski, M.; Santini, P. M.
3
2004
Stability of flexible spacecrafts. Zbl 0368.70035
Santini, Paolo
3
1976
Integrable functional equations and algebraic geometry. Zbl 0815.39008
Dubrovin, B. A.; Fokas, A. S.; Santini, P. M.
3
1994
Solvable nonlinear algebraic equations. Zbl 0737.35107
Santini, P. M.
3
1990
On the initial value problem for a class of nonlinear integral evolution equations including the sine-Hilbert equation. Zbl 0637.45007
Santini, P. M.; Ablowitz, M. J.; Fokas, A. S.
3
1987
Recursion operator and bi-Hamiltonian structure integrable multidimensional lattices. Zbl 0656.70020
Ragnisco, O.; Santini, P. M.
3
1988
Dimensional deformations of integrable systems. I: An approach to integrability in multidimensions. Zbl 0692.35088
Santini, P. M.
3
1989
Schlesinger transformations for discrete second Painlevé equation: d-\(P_{II}\). Zbl 1136.39302
Muğan, Uğurhan; Sakka, Ayman; Santini, Paolo M.
3
2005
Integrable singular integral evolution equations. Zbl 0924.35146
Santini, P. M.
3
1993
Towards a theory of chaos explained as travel on Riemann surfaces. Zbl 1153.37349
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
3
2009
Understanding complex dynamics by means of an associated Riemann surface. Zbl 1280.37052
Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.; Calogero, F.
3
2012
The finite-gap method and the periodic Cauchy problem for \((2+1)\)-dimensional anomalous waves for the focusing Davey-Stewartson 2 equation. Zbl 1522.35465
Grinevich, Petr G.; Santini, Paolo M.
3
2022
On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks. Zbl 1358.37108
Santucci, F.; Santini, P. M.
3
2016
The initial-boundary value problem on the interval for the nonlinear Schrödinger equation. The algebro-geometric approach. I. Zbl 1076.37061
Grinevich, P. G.; Santini, P. M.
2
2004
Lifting surface in subsonic unsteady regime. Zbl 0956.76037
Santini, P.; Gasbarri, P.
2
1999
An initial-boundary value problem for the Davey-Stewartson 1 equation and coherent structures in multidimensions. Zbl 0755.35132
Santini, P. M.; Fokas, A. S.
2
1990
An example of \({\bar \partial}\) problem arising in a finite difference context: Direct and inverse problem for the discrete analog of the equation \(\psi _{xx}+u\psi =\sigma \psi _ y\). Zbl 0655.35058
Ragnisco, O.; Santini, P. M.; Chitlaru-Briggs, S.; Ablowitz, M. J.
2
1987
Bi-Hamiltonian formulations of the intermediate long wave equation. Zbl 0694.35157
Santini, P. M.
2
1989
Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator. Zbl 1118.81417
Nieszporski, M.; Santini, P. M.; Doliwa, A.
2
2004
Designing efficient dyadic operations for cryptographic applications. Zbl 1441.94069
Banegas, Gustavo; Barreto, Paulo S. L. M.; Persichetti, Edoardo; Santini, Paolo
2
2020
Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation. Zbl 1284.35368
Grinevich, P. G.; Santini, P. M.
2
2013
On the computational hardness of the code equivalence problem in cryptography. Zbl 1520.94039
Barenghi, Alessandro; Biasse, Jean-François; Persichetti, Edoardo; Santini, Paolo
2
2023
The periodic \(N\) breather anomalous wave solution of the Davey-Stewartson equations; first appearance, recurrence, and blow up properties. Zbl 1531.35115
Coppini, F.; Grinevich, P. G.; Santini, P. M.
2
2024
Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz-Ladik lattices. Zbl 07787467
Coppini, F.; Santini, P. M.
2
2024
Initial-boundary value problems for linear PDEs: the analyticity approach. Zbl 1064.35153
Degasperis, A.; Manakov, S. V.; Santini, P. M.
1
2004
The self-adjoint 5-point and 7-point difference operators, the associated Dirichlet problems, Darboux transformations and Lelieuvre formulae. Zbl 1129.37343
Nieszporski, M.; Santini, P. M.
1
2005
Linear theories, hidden variables and integrable nonlinear equations. Zbl 1073.37539
Santini, Paolo Maria
1
1996
Symmetries and bi-Hamiltonian structures of 2+1 dimensional systems. Zbl 0736.35121
Santini, P. M.; Fokas, A. S.
1
1987
Structural dynamics of a cantilever swept wing. Zbl 0624.73061
Santini, P.; Sneider, M. A.; Leuzzi, L.
1
1986
A minicomputer finite elements program for microgravity hydroelastic analysis. Zbl 0515.73075
Santini, P.; Barboni, R.
1
1983
Ottimizzazione strutturale in campo dinamico. Zbl 0492.73098
Barboni, R.; Carlini, O.; Santini, P.
1
1981
On the occurrence of gauge-dependent secularities in nonlinear gravitational waves. Zbl 1373.83030
Briscese, Fabio; Santini, Paolo Maria
1
2017
The multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I. Zbl 1184.35309
Santini, Paolo Maria
1
2010
Cryptanalysis of a code-based full-time signature. Zbl 1472.94067
Aragon, Nicolas; Baldi, Marco; Deneuville, Jean-Christophe; Khathuria, Karan; Persichetti, Edoardo; Santini, Paolo
1
2021
Motion of orbiting spacecrafts with a sloshing fluid. Zbl 0412.76012
Santini, P.; Barboni, R.
1
1978
The integrable dynamics of a discrete curve. Zbl 0859.58018
Doliwa, Adam; Santini, Paolo Maria
1
1996
An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects. Zbl 1362.37141
Grinevich, P. G.; Santini, Paolo M.
1
2016
Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes. Zbl 1518.94089
Santini, Paolo; Baldi, Marco; Chiaraluce, Franco
1
2018
On the hardness of the Lee syndrome decoding problem. Zbl 1529.94057
Weger, Violetta; Khathuria, Karan; Horlemann, Anna-Lena; Battaglioni, Massimo; Santini, Paolo; Persichetti, Edoardo
1
2024
The periodic \(N\) breather anomalous wave solution of the Davey-Stewartson equations; first appearance, recurrence, and blow up properties. Zbl 1531.35115
Coppini, F.; Grinevich, P. G.; Santini, P. M.
2
2024
Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz-Ladik lattices. Zbl 07787467
Coppini, F.; Santini, P. M.
2
2024
On the hardness of the Lee syndrome decoding problem. Zbl 1529.94057
Weger, Violetta; Khathuria, Karan; Horlemann, Anna-Lena; Battaglioni, Massimo; Santini, Paolo; Persichetti, Edoardo
1
2024
On the computational hardness of the code equivalence problem in cryptography. Zbl 1520.94039
Barenghi, Alessandro; Biasse, Jean-François; Persichetti, Edoardo; Santini, Paolo
2
2023
The finite-gap method and the periodic Cauchy problem for \((2+1)\)-dimensional anomalous waves for the focusing Davey-Stewartson 2 equation. Zbl 1522.35465
Grinevich, Petr G.; Santini, Paolo M.
3
2022
LESS-FM: fine-tuning signatures from the code equivalence problem. Zbl 1485.94128
Barenghi, Alessandro; Biasse, Jean-François; Persichetti, Edoardo; Santini, Paolo
9
2021
The linear and nonlinear instability of the Akhmediev breather. Zbl 1477.35240
Grinevich, P. G.; Santini, P. M.
6
2021
Cryptanalysis of a code-based full-time signature. Zbl 1472.94067
Aragon, Nicolas; Baldi, Marco; Deneuville, Jean-Christophe; Khathuria, Karan; Persichetti, Edoardo; Santini, Paolo
1
2021
LESS is more: code-based signatures without syndromes. Zbl 1504.94204
Biasse, Jean-François; Micheli, Giacomo; Persichetti, Edoardo; Santini, Paolo
15
2020
Cryptanalysis of LEDAcrypt. Zbl 1504.94093
Apon, Daniel; Perlner, Ray; Robinson, Angela; Santini, Paolo
6
2020
Designing efficient dyadic operations for cryptographic applications. Zbl 1441.94069
Banegas, Gustavo; Barreto, Paulo S. L. M.; Persichetti, Edoardo; Santini, Paolo
2
2020
The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes. Zbl 1454.35340
Grinevich, P. G.; Santini, P. M.
11
2019
A reaction attack against cryptosystems based on LRPC codes. Zbl 1453.94112
Samardjiska, Simona; Santini, Paolo; Persichetti, Edoardo; Banegas, Gustavo
9
2019
Analysis of reaction and timing attacks against cryptosystems based on sparse parity-check codes. Zbl 07808958
Santini, Paolo; Battaglioni, Massimo; Chiaraluce, Franco; Baldi, Marco
1
2019
LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes. Zbl 1425.94046
Baldi, Marco; Barenghi, Alessandro; Chiaraluce, Franco; Pelosi, Gerardo; Santini, Paolo
21
2018
The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes. Zbl 1383.35210
Grinevich, P. G.; Santini, P. M.
15
2018
The periodic Cauchy problem for PT-symmetric NLS. I: The first appearance of rogue waves, regular behavior or blow up at finite times. Zbl 1411.35244
Santini, P. M.
12
2018
Numerical instability of the Akhmediev breather and a finite-gap model of it. Zbl 1477.37081
Grinevich, P. G.; Santini, P. M.
7
2018
Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case. Zbl 1408.35172
Grinevich, P. G.; Santini, P. M.
6
2018
Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes. Zbl 1518.94089
Santini, Paolo; Baldi, Marco; Chiaraluce, Franco
1
2018
On the occurrence of gauge-dependent secularities in nonlinear gravitational waves. Zbl 1373.83030
Briscese, Fabio; Santini, Paolo Maria
1
2017
Nonlocality and the inverse scattering transform for the Pavlov equation. Zbl 1344.35126
Grinevich, P. G.; Santini, P. M.
4
2016
On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks. Zbl 1358.37108
Santucci, F.; Santini, P. M.
3
2016
An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects. Zbl 1362.37141
Grinevich, P. G.; Santini, Paolo M.
1
2016
The Cauchy problem for the Pavlov equation. Zbl 1332.35324
Grinevich, P. G.; Santini, P. M.; Wu, D.
6
2015
The inverse spectral transform for the Dunajski hierarchy and some of its reductions: I. Cauchy problem and longtime behavior of solutions. Zbl 1331.35313
Yi, G.; Santini, P. M.
5
2015
Geometry of Winter model. Zbl 1356.81163
Aglietti, U. G.; Santini, P. M.
4
2015
Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation. Zbl 1284.35368
Grinevich, P. G.; Santini, P. M.
2
2013
Wave breaking in solutions of the dispersionless Kadomtsev-Petviashvili equation at a finite time. Zbl 1352.35148
Manakov, S. V.; Santini, P. M.
9
2012
Understanding complex dynamics by means of an associated Riemann surface. Zbl 1280.37052
Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.; Calogero, F.
3
2012
On the dispersionless Kadomtsev-Petviashvili equation in \(n+1\) dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking. Zbl 1241.35181
Manakov, S. V.; Santini, P. M.
16
2011
Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking. Zbl 1226.35064
Manakov, S. V.; Santini, P. M.
8
2011
The multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I. Zbl 1184.35309
Santini, Paolo Maria
1
2010
On the solutions of the second heavenly and Pavlov equations. Zbl 1184.35279
Manakov, S. V.; Santini, P. M.
20
2009
The dispersionless 2D Toda equation: Dressing, Cauchy problem, longtime behaviour, implicit solutions and wave breaking. Zbl 1165.37039
Manakov, S. V.; Santini, P. M.
9
2009
Towards a theory of chaos explained as travel on Riemann surfaces. Zbl 1153.37349
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
3
2009
On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking. Zbl 1136.35083
Manakov, S. V.; Santini, P. M.
25
2008
The remarkable relations among PDEs integrable by the inverse spectral transform method, by the method of characteristics and by the Hopf-Cole transformation. Zbl 1140.37020
Zenchuk, A. I.; Santini, P. M.
5
2008
A hierarchy of integrable partial differential equations in \(2+1\) dimensions associated with one-parameter families of one-dimensional vector fields. Zbl 1131.37061
Manakov, S. V.; Santini, P. M.
23
2007
Integrable lattices and their sublattices: from the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme. Zbl 1121.37058
Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.
13
2007
Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals. Zbl 1126.37040
Grinevich, P. G.; Santini, P. M.
12
2007
The general solution of the matrix equation \(w_t + \sum^n_{k=1} w_{x_k}\rho^{(k)}(w) = \rho (w) + [w, T \tilde{\rho}(w)]\). Zbl 1209.15022
Santini, P. M.; Zenchuk, A. I.
8
2007
Dressing method based on the homogeneous Fredholm equation: quasilinear PDEs in multidimensions. Zbl 1123.35074
Zenchuk, A. I.; Santini, P. M.
6
2007
Integrable lattices and their sublattices. II: From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices. Zbl 1152.81403
Doliwa, A.; Nieszporski, M.; Santini, P. M.
4
2007
Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation. Zbl 1236.37042
Manakov, S. V.; Santini, P. M.
40
2006
Partially integrable systems in multi-dimensions by a variant of the dressing method. I. Zbl 1122.37053
Zenchuk, A. I.; Santini, P. M.
4
2006
The transition from regular to irregular motions, explained as travel on Riemann surfaces. Zbl 1157.70309
Calogero, F.; Gómez-Ullate, D.; Santini, P. M.; Sommacal, M.
17
2005
Integrable and nonintegrable initial boundary value problems for soliton equations. Zbl 1362.35249
Degasperis, A.; Manakov, S. V.; Santini, P. M.
4
2005
Schlesinger transformations for discrete second Painlevé equation: d-\(P_{II}\). Zbl 1136.39302
Muğan, Uğurhan; Sakka, Ayman; Santini, Paolo M.
3
2005
The self-adjoint 5-point and 7-point difference operators, the associated Dirichlet problems, Darboux transformations and Lelieuvre formulae. Zbl 1129.37343
Nieszporski, M.; Santini, P. M.
1
2005
Geometric discretization of the Bianchi system. Zbl 1087.53020
Doliwa, A.; Nieszporski, M.; Santini, P. M.
3
2004
The initial-boundary value problem on the interval for the nonlinear Schrödinger equation. The algebro-geometric approach. I. Zbl 1076.37061
Grinevich, P. G.; Santini, P. M.
2
2004
Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator. Zbl 1118.81417
Nieszporski, M.; Santini, P. M.; Doliwa, A.
2
2004
Initial-boundary value problems for linear PDEs: the analyticity approach. Zbl 1064.35153
Degasperis, A.; Manakov, S. V.; Santini, P. M.
1
2004
Asymptotic lattices and their integrable reductions. I: The Bianchi-Ernst and the Fubini-Ragazzi lattices. Zbl 1001.37073
Doliwa, A.; Nieszporski, M.; Santini, P. M.
7
2001
Transformations of quadrilateral lattices. Zbl 0987.37070
Doliwa, Adam; Santini, Paolo Maria; Mañas, Manuel
38
2000
The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice. Zbl 0997.37052
Doliwa, Adam; Santíni, Paolo Maria
20
2000
Charged free fermions, vertex operators and the classical theory of conjugate nets. Zbl 1041.81058
Doliwa, Adam; Mañas, Manuel; Martínez Alonso, Luis; Medina, Elena; Santini, Paolo Maria
12
1999
Geometry of discrete curves and lattices and integrable difference equations. Zbl 0935.53002
Doliwa, Adam; Santini, Paolo Maria
5
1999
Lifting surface in subsonic unsteady regime. Zbl 0956.76037
Santini, P.; Gasbarri, P.
2
1999
\(\bar \partial\)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice. Zbl 0908.35125
Doliwa, A.; Manakov, S. V.; Santini, P. M.
21
1998
Multidimensional quadrilateral lattices are integrable. Zbl 1044.37528
Doliwa, Adam; Santini, Paolo Maria
65
1997
The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices. Zbl 0969.37528
Cieśliński, Jan; Doliwa, Adam; Santini, Paolo Maria
30
1997
Darboux transformations for multidimensional quadrilateral lattices. I. Zbl 1006.37501
Mañas, Manuel; Doliwa, Adam; Santini, Paolo Maria
29
1997
Multiple-scale perturbation beyond the nonlinear Schrödinger equation. I. Zbl 0890.35139
Degasperis, A.; Manakov, S. V.; Santini, P. M.
16
1997
Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction. Zbl 0962.35510
Mañas, Manuel; Santini, Paolo Maria
15
1997
Linear theories, hidden variables and integrable nonlinear equations. Zbl 1073.37539
Santini, Paolo Maria
1
1996
The integrable dynamics of a discrete curve. Zbl 0859.58018
Doliwa, Adam; Santini, Paolo Maria
1
1996
Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy. Zbl 0827.58024
Doliwa, Adam; Santini, Paolo Maria
34
1995
An elementary geometric characterization of the integrable motions of a curve. Zbl 0941.37532
Doliwa, A.; Santini, P. M.
65
1994
Cellular automata in \(1+1\), \(2+1\) and \(3+1\) dimensions, constants of motion and coherent structures. Zbl 0809.58021
Bruschi, M.; Santini, P. M.
5
1994
Integrable functional equations and algebraic geometry. Zbl 0815.39008
Dubrovin, B. A.; Fokas, A. S.; Santini, P. M.
3
1994
Integrable singular integral evolution equations. Zbl 0924.35146
Santini, P. M.
3
1993
Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter. Zbl 0761.35094
Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P. M.
7
1992
Integrable nonlinear evolution equations with constraints: I. Zbl 0762.35104
Santini, P. M.
6
1992
Integrable symplectic maps. Zbl 0734.58023
Bruschi, M.; Ragnisco, O.; Santini, P. M.; Tu, Guizhang
75
1991
Nonlocal integrable partners to generalized MKdV and two-dimensional Toda lattice equation in the formalism of a dressing method with quantized spectral parameter. Zbl 0739.35090
Degasperis, A.; Lebedev, D.; Olshanetskii, M.; Pakulyak, S.; Perelomov, A.; Santini, P.
13
1991
Dromions and a boundary value problem for the Davey-Stewartson 1 equation. Zbl 0707.35144
Fokas, A. S.; Santini, P. M.
73
1990
Energy exchange of interacting coherent structures in multidimensions. Zbl 0696.35180
Santini, P. M.
14
1990
A unified algebraic approach to integral and discrete evolution equations. Zbl 0725.45005
Ragnisco, O.; Santini, P. M.
12
1990
Solvable nonlinear algebraic equations. Zbl 0737.35107
Santini, P. M.
3
1990
An initial-boundary value problem for the Davey-Stewartson 1 equation and coherent structures in multidimensions. Zbl 0755.35132
Santini, P. M.; Fokas, A. S.
2
1990
Dimensional deformations of integrable systems. I: An approach to integrability in multidimensions. Zbl 0692.35088
Santini, P. M.
3
1989
Bi-Hamiltonian formulations of the intermediate long wave equation. Zbl 0694.35157
Santini, P. M.
2
1989
Recursion operators and bi-Hamiltonian structures in multidimensions. I. Zbl 0674.35074
Santini, P. M.; Fokas, A. S.
67
1988
Recursion operators and bi-Hamiltonian structures in multidimensions. II. Zbl 0706.35129
Fokas, A. S.; Santini, P. M.
67
1988
Bi-Hamiltonian formulation of the Kadomtsev-Petviashvili and Benjamin-Ono equations. Zbl 0695.35184
Fokas, A. S.; Santini, P. M.
14
1988
Recursion operator and bi-Hamiltonian structure integrable multidimensional lattices. Zbl 0656.70020
Ragnisco, O.; Santini, P. M.
3
1988
On the initial value problem for a class of nonlinear integral evolution equations including the sine-Hilbert equation. Zbl 0637.45007
Santini, P. M.; Ablowitz, M. J.; Fokas, A. S.
3
1987
An example of \({\bar \partial}\) problem arising in a finite difference context: Direct and inverse problem for the discrete analog of the equation \(\psi _{xx}+u\psi =\sigma \psi _ y\). Zbl 0655.35058
Ragnisco, O.; Santini, P. M.; Chitlaru-Briggs, S.; Ablowitz, M. J.
2
1987
Symmetries and bi-Hamiltonian structures of 2+1 dimensional systems. Zbl 0736.35121
Santini, P. M.; Fokas, A. S.
1
1987
The recursion operator of the Kadomtsev-Petviashvili equation and the squared eigenfunctions of the Schrödinger operator. Zbl 0613.35073
Fokas, A. S.; Santini, P. M.
30
1986
Structural dynamics of a cantilever swept wing. Zbl 0624.73061
Santini, P.; Sneider, M. A.; Leuzzi, L.
1
1986
Nonlinear evolution equations associated with a Riemann-Hilbert scattering problem. Zbl 0581.35075
Degasperis, A.; Santini, P. M.; Ablowitz, M. J.
8
1985
The direct linearization of a class of nonlinear evolution equations. Zbl 0557.35111
Santini, P. M.; Ablowitz, M. J.; Fokas, A. S.
22
1984
On the limit from the intermediate long wave equation to the Benjamin-Ono equation. Zbl 0543.45008
Santini, P. M.; Ablowitz, M. J.; Fokas, A. S.
21
1984
A minicomputer finite elements program for microgravity hydroelastic analysis. Zbl 0515.73075
Santini, P.; Barboni, R.
1
1983
Integrable three-dimensional lattices. Zbl 0481.35046
Levi, D.; Pilloni, L.; Santini, P. M.
22
1981
Ottimizzazione strutturale in campo dinamico. Zbl 0492.73098
Barboni, R.; Carlini, O.; Santini, P.
1
1981
Motion of orbiting spacecrafts with a sloshing fluid. Zbl 0412.76012
Santini, P.; Barboni, R.
1
1978
...and 1 more Documents
all top 5

Cited by 876 Authors

48 Santini, Paolo Maria
27 Doliwa, Adam
21 Fokas, Athanassios S.
17 Mañas, Manuel
17 Nijhoff, Frank W.
15 Grinevich, Pëtr Georgievich
14 Konopelchenko, Boris Georgievich
14 Qu, Changzheng
12 Sahadevan, Ramajayam
11 He, Jingsong
10 Calogero, Francesco A.
10 Gubbiotti, Giorgio
9 Hu, Xingbiao
9 Lakshmanan, Muthusamy
9 Nieszporski, Maciej
9 Prykarpatsky, Anatoliy Karolevych
9 Schief, Wolfgang Karl
9 Zhang, Dajun
8 Capel, Hans W.
8 Ferapontov, Evgeny Vladimirovich
8 Hone, Andrew N. W.
8 Klein, Christian
8 Persichetti, Edoardo
8 Prykarpatsky, Yarema Anatoliyovych
8 Suris, Yuri Borisovich
7 Ablowitz, Mark Jay
7 Biondini, Gino
7 Bobenko, Alexander Ivanovich
7 Bogdanov, Leonid Vital’evich
7 Fu, Wei
7 Morozov, Oleg I.
7 Radha, Ramaswamy
7 Zenchuk, Alexandre I.
6 Cieśliński, Jan L.
6 Dunajski, Maciej
6 Fan, Engui
6 Kassotakis, Pavlos G.
6 Maccari, Attilio
6 Pavlov, Maxim V.
6 Quispel, Gilles Reinout Willem
6 Scimiterna, Christian
6 Strampp, Walter
6 Xu, Xixiang
5 Adler, Vsevolod Eduardovich
5 Ariznabarreta, Gerardo
5 Cao, Cewen
5 Degasperis, Antonio
5 Du, Dianlou
5 Geng, Xianguo
5 Levi, Decio
5 Li, Chuanzhong
5 Lou, Senyue
5 Matsuno, Yoshimasa
5 Ohta, Yasuhiro
5 Pashaev, Oktay K.
5 Pelinovsky, Dmitry Efimovich
5 Pempinelli, Flora
5 Sergyeyev, Artur
5 Tian, Shoufu
4 Baldi, Marco
4 Boiti, Marco
4 Chang, Xiangke
4 Cheng, Yi
4 Dubrovsky, V. G.
4 Feng, Baofeng
4 Grava, Tamara
4 Guil, Francisco
4 Hentosh, Oksana E.
4 Kajiwara, Kenji
4 Li, Biao
4 Luo, Jinghua
4 Ma, Wen-Xiu
4 Martínez Alonso, Luis
4 Matsuura, Nozomu
4 Myrzakulov, Ratbay
4 Odesskii, Alexander
4 Ragnisco, Orlando
4 Satsuma, Junkichi
4 Saut, Jean-Claude
4 Sergeev, Sergeĭ Mikhaĭlovich
4 Shepelsky, Dmitry
4 Sokolov, Vladimir Vyacheslavovich
4 Stoilov, Nikola M.
4 Tam, Hon-Wah
4 Tu, Guizhang
4 van der Kamp, Peter H.
4 Zhang, Yingnan
4 Zhou, Ruguang
3 Anco, Stephen C.
3 Andrushkiw, Roman I.
3 Barenghi, Alessandro
3 Bender, Carl M.
3 Błaszak, Maciej
3 Boutet de Monvel, Anne Marie
3 Bruschi, Mario
3 Calini, Annalisa M.
3 Carroll, Robert Wayne
3 Chen, Dengyuan
3 Cheng, Jipeng
3 Cho, Joseph
...and 776 more Authors
all top 5

Cited in 170 Serials

113 Journal of Mathematical Physics
62 Physics Letters. A
41 Physica D
39 Theoretical and Mathematical Physics
33 Journal of Physics A: Mathematical and Theoretical
30 Journal of Geometry and Physics
25 Studies in Applied Mathematics
24 Journal of Nonlinear Mathematical Physics
23 Chaos, Solitons and Fractals
19 Communications in Mathematical Physics
14 Letters in Mathematical Physics
14 Physica A
13 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
9 Nonlinearity
8 Journal of Mathematical Analysis and Applications
8 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
7 Communications in Nonlinear Science and Numerical Simulation
6 Acta Applicandae Mathematicae
6 Designs, Codes and Cryptography
6 Chaos
5 Applicable Analysis
5 Mathematical Methods in the Applied Sciences
5 Wave Motion
5 Applied Mathematics Letters
5 Journal of Nonlinear Science
5 Journal of Mathematical Sciences (New York)
5 Communications in Theoretical Physics
5 Analysis and Mathematical Physics
4 Computers & Mathematics with Applications
4 Ukrainian Mathematical Journal
4 Reviews in Mathematical Physics
4 Mathematics and Computers in Simulation
4 Annals of Physics
4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
4 Journal of High Energy Physics
4 International Journal of Geometric Methods in Modern Physics
4 Advances in Mathematics of Communications
3 International Journal of Theoretical Physics
3 Journal of Fluid Mechanics
3 Advances in Mathematics
3 Applied Mathematics and Computation
3 Functional Analysis and its Applications
3 Geometriae Dedicata
3 Transactions of the American Mathematical Society
3 Differential Geometry and its Applications
3 Buletinul Academiei de Științe a Republicii Moldova. Matematica
3 Nonlinear Dynamics
3 Journal of Mathematical Cryptology
3 Science China. Mathematics
2 Modern Physics Letters B
2 International Journal of Modern Physics B
2 Nuclear Physics. B
2 Reports on Mathematical Physics
2 Duke Mathematical Journal
2 International Journal of Mathematics and Mathematical Sciences
2 Journal of Differential Equations
2 Journal of Optimization Theory and Applications
2 Meccanica
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Siberian Mathematical Journal
2 Advances in Mathematics (Beijing)
2 Discrete & Computational Geometry
2 Mathematical and Computer Modelling
2 Discrete Mathematics and Applications
2 Numerical Algorithms
2 Linear Algebra and its Applications
2 Journal of Computer and Systems Sciences International
2 Selecta Mathematica. New Series
2 Journal of Difference Equations and Applications
2 Mathematical Problems in Engineering
2 Regular and Chaotic Dynamics
2 Journal of Evolution Equations
2 Central European Journal of Mathematics
2 Foundations of Physics
2 Frontiers of Mathematics in China
2 European Journal of Mathematics
1 International Journal of Modern Physics A
1 Classical and Quantum Gravity
1 Communications on Pure and Applied Mathematics
1 Indian Journal of Pure & Applied Mathematics
1 Inverse Problems
1 Information Processing Letters
1 Journal d’Analyse Mathématique
1 Journal of Engineering Mathematics
1 Journal of the Franklin Institute
1 Mathematical Notes
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Periodica Mathematica Hungarica
1 Physics Letters. B
1 Reviews of Modern Physics
1 Rocky Mountain Journal of Mathematics
1 Russian Mathematical Surveys
1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
1 The Mathematical Intelligencer
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Information Sciences
1 Journal of Approximation Theory
1 Journal of Functional Analysis
1 Matematički Vesnik
1 Mathematische Zeitschrift
...and 70 more Serials
all top 5

Cited in 49 Fields

475 Dynamical systems and ergodic theory (37-XX)
401 Partial differential equations (35-XX)
103 Difference and functional equations (39-XX)
100 Differential geometry (53-XX)
93 Quantum theory (81-XX)
48 Information and communication theory, circuits (94-XX)
41 Mechanics of particles and systems (70-XX)
37 Fluid mechanics (76-XX)
34 Global analysis, analysis on manifolds (58-XX)
31 Statistical mechanics, structure of matter (82-XX)
30 Nonassociative rings and algebras (17-XX)
28 Numerical analysis (65-XX)
27 Algebraic geometry (14-XX)
25 Ordinary differential equations (34-XX)
24 Number theory (11-XX)
23 Special functions (33-XX)
16 Linear and multilinear algebra; matrix theory (15-XX)
14 Relativity and gravitational theory (83-XX)
13 Geometry (51-XX)
13 Mechanics of deformable solids (74-XX)
13 Optics, electromagnetic theory (78-XX)
12 Convex and discrete geometry (52-XX)
10 Functions of a complex variable (30-XX)
8 Harmonic analysis on Euclidean spaces (42-XX)
8 Computer science (68-XX)
6 Associative rings and algebras (16-XX)
6 Topological groups, Lie groups (22-XX)
6 Integral equations (45-XX)
5 Combinatorics (05-XX)
5 Commutative algebra (13-XX)
5 Approximations and expansions (41-XX)
5 Operator theory (47-XX)
4 Calculus of variations and optimal control; optimization (49-XX)
3 History and biography (01-XX)
3 Functional analysis (46-XX)
3 Manifolds and cell complexes (57-XX)
2 Group theory and generalizations (20-XX)
2 Measure and integration (28-XX)
2 Integral transforms, operational calculus (44-XX)
2 Probability theory and stochastic processes (60-XX)
2 Geophysics (86-XX)
2 Operations research, mathematical programming (90-XX)
1 Mathematical logic and foundations (03-XX)
1 Field theory and polynomials (12-XX)
1 \(K\)-theory (19-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Statistics (62-XX)
1 Biology and other natural sciences (92-XX)
1 Systems theory; control (93-XX)

Citations by Year