## Grinevich, Pëtr Georgievich

Compute Distance To:
 Author ID: grinevich.petr-georgievich Published as: Grinevich, P. G.; Grinevich, Petr G.; Grinevich, Piotr G.; Grinevich, P. more...less Further Spellings: Piotr G. Grinevich Homepage: http://pgg.itp.ac.ru/ External Links: MGP · Wikidata · Math-Net.Ru
 Documents Indexed: 73 Publications since 1982 Co-Authors: 38 Co-Authors with 62 Joint Publications 1,448 Co-Co-Authors
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### Co-Authors

 11 single-authored 22 Novikov, Sergeĭ Petrovich 12 Novikov, Roman G. 12 Santini, Paolo Maria 6 Abenda, Simonetta 5 Mironov, Andreĭ Evgen’evich 4 Schmidt, Martin Ulrich 3 Taimanov, Iskander Asanovich 2 Bukhshtaber, Viktor Matveevich 2 Orlov, Aleksandr Yu. 1 Adler, Vsevolod Eduardovich 1 Berest, Yuri Yu. 1 Chalykh, Oleg A. 1 Chekhov, Leonid O. 1 Dobrokhotov, Sergei Yurievich 1 Doliwa, Adam 1 Dubrovin, Boris Anatol’evich 1 Etingof, Pavel Il’ich 1 Feigin, Misha V. 1 Felder, J. 1 Ferapontov, Evgeny Vladimirovich 1 Grushevsky, S. M. 1 Kaipa, Krishna V. 1 Krichever, Igor’ Moiseevich 1 Manakov, S. V. 1 Marshakov, Andrei V. 1 Nekrasov, Nikita Alexandrovich 1 Nieszporski, Maciej 1 Okun’kov, Andreĭ Yur’evich 1 Olshanetsky, Mikhail A. 1 Pogrebkov, Andrei K. 1 Schulman, E. I. 1 Sergeev, Aleksandr Nikolaevich 1 Sheĭnman, Oleg Karlovich 1 Shlosman, Senya B. 1 Tsfasman, Michael A. 1 Varchenko, Alexander Nikolaevich 1 Veselov, Alexander Petrovich 1 Zabrodin, Anton V.
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### Serials

 13 Russian Mathematical Surveys 8 Functional Analysis and its Applications 7 Theoretical and Mathematical Physics 3 Journal of Mathematical Physics 3 Letters in Mathematical Physics 3 Physica D 2 Communications in Mathematical Physics 2 Nonlinearity 2 Physics Letters. A 2 Journal of Geometry and Physics 2 Soviet Mathematics. Doklady 2 Proceedings of the Steklov Institute of Mathematics 1 Communications on Pure and Applied Mathematics 1 Advances in Mathematics 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Journal of Differential Equations 1 Mathematics of the USSR. Izvestiya 1 Studies in Applied Mathematics 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 St. Petersburg Mathematical Journal 1 Selecta Mathematica. New Series 1 Bulletin des Sciences Mathématiques 1 Doklady Mathematics 1 Bulletin of the Brazilian Mathematical Society. New Series
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### Fields

 47 Partial differential equations (35-XX) 38 Dynamical systems and ergodic theory (37-XX) 11 Quantum theory (81-XX) 10 Algebraic geometry (14-XX) 10 Operator theory (47-XX) 7 Functions of a complex variable (30-XX) 7 Ordinary differential equations (34-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Differential geometry (53-XX) 4 Fluid mechanics (76-XX) 3 Difference and functional equations (39-XX) 2 History and biography (01-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Mechanics of particles and systems (70-XX) 2 Optics, electromagnetic theory (78-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX)

### Citations contained in zbMATH Open

63 Publications have been cited 400 times in 256 Documents Cited by Year
Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I: Energies below the ground state. Zbl 0672.35074
Grinevich, P. G.; Novikov, S. P.
1988
Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity. Zbl 1022.81057
Grinevich, P. G.
2000
Inverse scattering problem for the two-dimensional Schrödinger operator, the $${\bar\partial}$$-method and nonlinear equations. Zbl 0617.35031
Grinevich, P. G.; Manakov, S. V.
1986
Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials. Zbl 0843.35090
Grinevich, Piotr G.; Novikov, Roman G.
1995
Spectral conservation laws for periodic nonlinear equations of the Melnikov type. Zbl 1158.35078
Grinevich, P. G.; Taimanov, I. A.
2008
Rational solutions for the equation of commutation of differential operators. Zbl 0514.47034
Grinevich, P. G.
1982
Rational degenerations of $${\mathtt M}$$-curves, totally positive Grassmannians and KP2-solitons. Zbl 1400.14094
Abenda, Simonetta; Grinevich, Petr G.
2018
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.
2007
Conformal invariant functionals of immersions of tori into $$\mathbb{R}^3$$. Zbl 0949.53007
Grinevich, P. G.; Schmidt, M. U.
1998
Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations. Zbl 1194.35345
Grinevich, P. G.; Schmidt, M. U.
1995
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.
2007
Analogues of multisoliton potentials for the two-dimensional Schrödinger operator, and a nonlocal Riemann problem. Zbl 0616.35071
Grinevich, P. G.; Novikov, R. G.
1986
Rational solitons of the Veselov-Novikov equations are reflectionless two-dimensional potentials at fixed energy. Zbl 0617.35121
Grinevich, P. G.
1986
Faddeev eigenfunctions for point potentials in two dimensions. Zbl 1255.81137
Grinevich, P. G.; Novikov, R. G.
2012
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.
2018
Spectral theory of commuting operators of rank two with periodic coefficients. Zbl 0514.47035
Novikov, S. P.; Grinevich, P. G.
1982
Moutard transform for generalized analytic functions. Zbl 1358.30019
Grinevich, P. G.; Novikov, R. G.
2016
2D-Schrödinger operator, $$(2+1)$$ evolution systems and new reductions, 2D-Burgers hierarchy and inverse problem data. Zbl 1231.35199
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2010
Analogs of multisoliton potentials for the two-dimensional Schrödinger operator. Zbl 0657.35122
Grinevich, P. G.; Novikov, R. G.
1985
Generalized analytic functions, Moutard-type transforms, and holomorphic maps. Zbl 1355.30041
Grinevich, P. G.; Novikov, R. G.
2016
Reducible $$M$$-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons. Zbl 1426.37052
Abenda, Simonetta; Grinevich, Petr G.
2019
Real soliton lattices of the Kadomtsev-Petviashvili II equation and desingularization of spectral curves: the $$\mathrm{Gr}^{\mathrm{TP}}(2, 4)$$ case. Zbl 1437.37086
Abenda, Simonetta; Grinevich, Petr G.
2018
On the symmetries of integrable systems. Zbl 0816.35122
Grinevich, P. G.; Orlov, A. Yu.; Schulman, E. I.
1993
The Cauchy problem for the Pavlov equation. Zbl 1332.35324
Grinevich, P. G.; Santini, P. M.; Wu, D.
2015
Singular finite-gap operators and indefinite metrics. Zbl 1180.35384
Grinevich, P. G.; Novikov, S. P.
2009
Moutard transform approach to generalized analytic functions with contour poles. Zbl 1351.30034
Grinevich, P. G.; Novikov, R. G.
2016
Variations of the complex structure of Riemann surfaces by vector fields on a contour and objects of the KP theory. The Krichever-Novikov problem of the action on the Baker-Akhieser functions. Zbl 0719.30037
Grinevich, P. G.; Orlov, A. Yu.
1990
Real finite-zone solutions of the sine-Gordon equation: a formula for the topological charge. Zbl 1057.37066
Grinevich, P. G.; Novikov, S. P.
2001
Analogues of multisoliton potentials for the two-dimensional Schrödinger operator. Zbl 0606.35072
Grinevich, P. G.; Novikov, R. G.
1985
String equation. II: Physical solution. Zbl 0836.35142
Grinevich, P. G.; Novikov, S. P.
1994
Nonselfintersecting magnetic orbits on the plane. Proof of the overthrowing of cycles principle. Zbl 0852.58017
Grinevich, P. G.; Novikov, S. P.
1995
Nonlocality and the inverse scattering transform for the Pavlov equation. Zbl 1344.35126
Grinevich, P. G.; Santini, P. M.
2016
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.
2019
Moutard transforms for the conductivity equation. Zbl 1430.35227
Grinevich, P. G.; Novikov, R. G.
2019
Nonsingularity of the direct scattering transform for the KP II equation with a real exponentially decaying-at-infinity potential. Zbl 0879.35144
Grinevich, P. G.
1997
The Cauchy kernel for the Novikov-Dynnikov DN-discrete complex analysis in triangular lattices. Zbl 1141.39019
Grinevich, P. G.; Novikov, R. G.
2007
The linear and nonlinear instability of the Akhmediev breather. Zbl 1477.35240
Grinevich, P. G.; Santini, P. M.
2021
Singular solitons and indefinite metrics. Zbl 1248.34132
Grinevich, P. G.; Novikov, S. P.
2011
Singular soliton operators and indefinite metrics. Zbl 1319.34153
Grinevich, Petr G.; Novikov, Sergey P.
2013
Vector rank of commuting matrix differential operators. Proof of S. P. Novikov’s criterion. Zbl 0623.47049
Grinevich, P. G.
1987
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.
2004
Approximation theorem for the self-focusing nonlinear Schrödinger equation and for the periodic curves in $$\mathbb{R}^3$$. Zbl 0981.35082
Grinevich, P. G.
2001
Topological charge of the real periodic finite-gap sine-Gordon solutions. Zbl 1044.35071
Grinevich, P. G.; Novikov, S. P.
2003
Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation. Zbl 1284.35368
Grinevich, P. G.; Santini, P. M.
2013
Discrete $$SL_{n}$$-connections and self-adjoint difference operators on 2-dimensional manifolds. Zbl 1282.39006
Grinevich, P. G.; Novikov, S. P.
2013
Infinitesimal Darboux transformations of the spectral curves of tori in the four-space. Zbl 1141.53009
Grinevich, P. G.; Taimanov, I. A.
2007
Spectrally meromorphic operators and non-linear systems. Zbl 1320.47046
Grinevich, P. G.; Novikov, S. P.
2014
Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case. Zbl 1408.35172
Grinevich, P. G.; Santini, P. M.
2018
Numerical instability of the Akhmediev breather and a finite-gap model of it. Zbl 1477.37081
Grinevich, P. G.; Santini, P. M.
2018
Creation and annihilation of point-potentials using Moutard-type transform in spectral variable. Zbl 1454.81064
Grinevich, P. G.; Novikov, R. G.
2020
Commuting matrix differential operators of arbitrary rank. Zbl 0598.47049
Grinevich, P. G.
1984
Closed curves in $$\mathbb{R}^3$$ and the nonlinear Schrödinger equation. Zbl 0964.35149
Grinevich, P. G.; Schmidt, M. U.
2000
Rapidly decreasing potentials on a background of finite-zone potentials and the $$\bar\partial$$-problem on Riemann surfaces. Zbl 0748.35025
Grinevich, P. G.
1989
Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations. Zbl 0848.35113
Grinevich, P. G.
1994
Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-1/2 particles. Zbl 1255.81136
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2010
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.
2016
On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator. Zbl 1330.81080
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2015
On $$s$$-meromorphic ordinary differential operators. Zbl 1418.34159
Grinevich, P. G.; Novikov, S. P.
2016
Erratum to: “Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-1/2 particles”. Zbl 1278.81065
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2011
Periodic billiard orbits on $$n$$-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations. Zbl 1205.14047
Abenda, Simonetta; Grinevich, Petr G.
2010
Inverse scattering problem for the two-dimensional Schrödinger operator at a fixed negative energy and generalized analytic functions. Zbl 0704.35137
Grinevich, P. G.; Novikov, S. P.
1988
Topological phenomena in the real periodic sine-Gordon theory. Zbl 1062.35114
Grinevich, P. G.; Novikov, S. P.
2003
Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians. Zbl 1492.14087
Abenda, Simonetta; Grinevich, Petr G.
2022
Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians. Zbl 1492.14087
Abenda, Simonetta; Grinevich, Petr G.
2022
The linear and nonlinear instability of the Akhmediev breather. Zbl 1477.35240
Grinevich, P. G.; Santini, P. M.
2021
Creation and annihilation of point-potentials using Moutard-type transform in spectral variable. Zbl 1454.81064
Grinevich, P. G.; Novikov, R. G.
2020
Reducible $$M$$-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons. Zbl 1426.37052
Abenda, Simonetta; Grinevich, Petr G.
2019
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.
2019
Moutard transforms for the conductivity equation. Zbl 1430.35227
Grinevich, P. G.; Novikov, R. G.
2019
Rational degenerations of $${\mathtt M}$$-curves, totally positive Grassmannians and KP2-solitons. Zbl 1400.14094
Abenda, Simonetta; Grinevich, Petr G.
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.
2018
Real soliton lattices of the Kadomtsev-Petviashvili II equation and desingularization of spectral curves: the $$\mathrm{Gr}^{\mathrm{TP}}(2, 4)$$ case. Zbl 1437.37086
Abenda, Simonetta; Grinevich, Petr G.
2018
Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case. Zbl 1408.35172
Grinevich, P. G.; Santini, P. M.
2018
Numerical instability of the Akhmediev breather and a finite-gap model of it. Zbl 1477.37081
Grinevich, P. G.; Santini, P. M.
2018
Moutard transform for generalized analytic functions. Zbl 1358.30019
Grinevich, P. G.; Novikov, R. G.
2016
Generalized analytic functions, Moutard-type transforms, and holomorphic maps. Zbl 1355.30041
Grinevich, P. G.; Novikov, R. G.
2016
Moutard transform approach to generalized analytic functions with contour poles. Zbl 1351.30034
Grinevich, P. G.; Novikov, R. G.
2016
Nonlocality and the inverse scattering transform for the Pavlov equation. Zbl 1344.35126
Grinevich, P. G.; Santini, P. M.
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.
2016
On $$s$$-meromorphic ordinary differential operators. Zbl 1418.34159
Grinevich, P. G.; Novikov, S. P.
2016
The Cauchy problem for the Pavlov equation. Zbl 1332.35324
Grinevich, P. G.; Santini, P. M.; Wu, D.
2015
On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator. Zbl 1330.81080
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2015
Spectrally meromorphic operators and non-linear systems. Zbl 1320.47046
Grinevich, P. G.; Novikov, S. P.
2014
Singular soliton operators and indefinite metrics. Zbl 1319.34153
Grinevich, Petr G.; Novikov, Sergey P.
2013
Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation. Zbl 1284.35368
Grinevich, P. G.; Santini, P. M.
2013
Discrete $$SL_{n}$$-connections and self-adjoint difference operators on 2-dimensional manifolds. Zbl 1282.39006
Grinevich, P. G.; Novikov, S. P.
2013
Faddeev eigenfunctions for point potentials in two dimensions. Zbl 1255.81137
Grinevich, P. G.; Novikov, R. G.
2012
Singular solitons and indefinite metrics. Zbl 1248.34132
Grinevich, P. G.; Novikov, S. P.
2011
Erratum to: “Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-1/2 particles”. Zbl 1278.81065
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2011
2D-Schrödinger operator, $$(2+1)$$ evolution systems and new reductions, 2D-Burgers hierarchy and inverse problem data. Zbl 1231.35199
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2010
Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-1/2 particles. Zbl 1255.81136
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2010
Periodic billiard orbits on $$n$$-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations. Zbl 1205.14047
Abenda, Simonetta; Grinevich, Petr G.
2010
Singular finite-gap operators and indefinite metrics. Zbl 1180.35384
Grinevich, P. G.; Novikov, S. P.
2009
Spectral conservation laws for periodic nonlinear equations of the Melnikov type. Zbl 1158.35078
Grinevich, P. G.; Taimanov, I. A.
2008
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.
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.
2007
The Cauchy kernel for the Novikov-Dynnikov DN-discrete complex analysis in triangular lattices. Zbl 1141.39019
Grinevich, P. G.; Novikov, R. G.
2007
Infinitesimal Darboux transformations of the spectral curves of tori in the four-space. Zbl 1141.53009
Grinevich, P. G.; Taimanov, I. A.
2007
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.
2004
Topological charge of the real periodic finite-gap sine-Gordon solutions. Zbl 1044.35071
Grinevich, P. G.; Novikov, S. P.
2003
Topological phenomena in the real periodic sine-Gordon theory. Zbl 1062.35114
Grinevich, P. G.; Novikov, S. P.
2003
Real finite-zone solutions of the sine-Gordon equation: a formula for the topological charge. Zbl 1057.37066
Grinevich, P. G.; Novikov, S. P.
2001
Approximation theorem for the self-focusing nonlinear Schrödinger equation and for the periodic curves in $$\mathbb{R}^3$$. Zbl 0981.35082
Grinevich, P. G.
2001
Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity. Zbl 1022.81057
Grinevich, P. G.
2000
Closed curves in $$\mathbb{R}^3$$ and the nonlinear Schrödinger equation. Zbl 0964.35149
Grinevich, P. G.; Schmidt, M. U.
2000
Conformal invariant functionals of immersions of tori into $$\mathbb{R}^3$$. Zbl 0949.53007
Grinevich, P. G.; Schmidt, M. U.
1998
Nonsingularity of the direct scattering transform for the KP II equation with a real exponentially decaying-at-infinity potential. Zbl 0879.35144
Grinevich, P. G.
1997
Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials. Zbl 0843.35090
Grinevich, Piotr G.; Novikov, Roman G.
1995
Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations. Zbl 1194.35345
Grinevich, P. G.; Schmidt, M. U.
1995
Nonselfintersecting magnetic orbits on the plane. Proof of the overthrowing of cycles principle. Zbl 0852.58017
Grinevich, P. G.; Novikov, S. P.
1995
String equation. II: Physical solution. Zbl 0836.35142
Grinevich, P. G.; Novikov, S. P.
1994
Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations. Zbl 0848.35113
Grinevich, P. G.
1994
On the symmetries of integrable systems. Zbl 0816.35122
Grinevich, P. G.; Orlov, A. Yu.; Schulman, E. I.
1993
Variations of the complex structure of Riemann surfaces by vector fields on a contour and objects of the KP theory. The Krichever-Novikov problem of the action on the Baker-Akhieser functions. Zbl 0719.30037
Grinevich, P. G.; Orlov, A. Yu.
1990
Rapidly decreasing potentials on a background of finite-zone potentials and the $$\bar\partial$$-problem on Riemann surfaces. Zbl 0748.35025
Grinevich, P. G.
1989
Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I: Energies below the ground state. Zbl 0672.35074
Grinevich, P. G.; Novikov, S. P.
1988
Inverse scattering problem for the two-dimensional Schrödinger operator at a fixed negative energy and generalized analytic functions. Zbl 0704.35137
Grinevich, P. G.; Novikov, S. P.
1988
Vector rank of commuting matrix differential operators. Proof of S. P. Novikov’s criterion. Zbl 0623.47049
Grinevich, P. G.
1987
Inverse scattering problem for the two-dimensional Schrödinger operator, the $${\bar\partial}$$-method and nonlinear equations. Zbl 0617.35031
Grinevich, P. G.; Manakov, S. V.
1986
Analogues of multisoliton potentials for the two-dimensional Schrödinger operator, and a nonlocal Riemann problem. Zbl 0616.35071
Grinevich, P. G.; Novikov, R. G.
1986
Rational solitons of the Veselov-Novikov equations are reflectionless two-dimensional potentials at fixed energy. Zbl 0617.35121
Grinevich, P. G.
1986
Analogs of multisoliton potentials for the two-dimensional Schrödinger operator. Zbl 0657.35122
Grinevich, P. G.; Novikov, R. G.
1985
Analogues of multisoliton potentials for the two-dimensional Schrödinger operator. Zbl 0606.35072
Grinevich, P. G.; Novikov, R. G.
1985
Commuting matrix differential operators of arbitrary rank. Zbl 0598.47049
Grinevich, P. G.
1984
Rational solutions for the equation of commutation of differential operators. Zbl 0514.47034
Grinevich, P. G.
1982
Spectral theory of commuting operators of rank two with periodic coefficients. Zbl 0514.47035
Novikov, S. P.; Grinevich, P. G.
1982
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### Cited by 248 Authors

 30 Grinevich, Pëtr Georgievich 22 Novikov, Roman G. 12 Santini, Paolo Maria 12 Taimanov, Iskander Asanovich 9 Novikov, Sergeĭ Petrovich 8 Abenda, Simonetta 7 Yakhshimuratov, Alisher Bekchanovich 6 Calogero, Francesco A. 6 Khasanov, Aknazar Bekdurdievich 5 Boiti, Marco 5 Mironov, Andreĭ Evgen’evich 5 Pempinelli, Flora 4 Agaltsov, Alexey D. 4 Babajanov, Bazar Atajanovich 4 Doliwa, Adam 4 Klein, Christian 4 Konopelchenko, Boris Georgievich 4 Lin, Runliang 4 Pogrebkov, Andrei K. 4 Previato, Emma 4 Santacesaria, Matteo 4 Siltanen, Samuli 4 Zheglov, Alexander B. 3 Adler, Mark 3 Bohle, Christoph 3 Dubrovsky, V. G. 3 Gesztesy, Fritz 3 Gómez-Ullate, David 3 Kazeykina, A. V. 3 Kazeykina, Anna 3 Lassas, Matti J. 3 Nakayashiki, Atsushi 3 Pedit, Franz J. 3 Pinkall, Ulrich 3 Topovsky, A. V. 3 Tsarev, Sergej Petrovich 3 Urazboev, Gayrat U. 3 van Moerbeke, Pierre 3 Vasilevskiĭ, B. O. 3 Veselov, Alexander Petrovich 3 Weikard, Rudi 3 Wu, Derchyi 2 Basalaev, M. Yu. 2 Bogdanov, Leonid Vital’evich 2 Bukhshtaber, Viktor Matveevich 2 Calini, Annalisa M. 2 Chang, Jen-Hsu 2 Davletshina, Valentina N. 2 Dubrovin, Boris Anatol’evich 2 Enolskiĭ, Viktor Zelikovich 2 Etingof, Pavel Il’ich 2 Fokas, Athanassios S. 2 Grava, Tamara 2 Hallnäs, Martin A. 2 Hohage, Thorsten 2 Hone, Andrew N. W. 2 Ivey, Thomas A. 2 Khenkin, Gennadiĭ Markovich 2 Kilian, Martin 2 Klibanov, Michael V. 2 Kriecherbauer, Thomas 2 Kudryavtsev, A. G. 2 Kurylëv, Yaroslav Vadimovich 2 Lakshtanov, Evgeny L. 2 Latham, Geoff A. 2 Leschke, Katrin 2 Leyvraz, Francois 2 Liu, Hanli 2 Manakov, S. V. 2 Mauleshova, Gulnara S. 2 Mueller, Jennifer L. 2 Muñoz, Claudio 2 Music, Michael 2 Nicoleau, François 2 Nieszporski, Maciej 2 Pantong, Natee 2 Perry, Peter A. 2 Prinari, Barbara 2 Rumyantseva, Olga D. 2 Salo, Mikko 2 Schmidt, Martin Ulrich 2 Shan, Hua 2 Shemyakova, Ekaterina 2 Shiota, Takahiro 2 Sommacal, Matteo 2 Su, Jianzhong 2 Tamminen, Janne P. 2 Tzou, Leo 2 Unterkofler, Karl 2 Vaĭnberg, Boris Rufimovich 2 Wright, Otis Clarence III 2 Zeng, Yunbo 1 Agostini, Daniele 1 Allanazarova, T. Zh. 1 Angelopoulos, Yannis 1 Arriagada, Waldo G. 1 Babadjanova, Aygul Kamildjanovna 1 Bahri, Abbas 1 Bakalov, Bojko 1 Barceló, Juan Antonio ...and 148 more Authors
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### Cited in 81 Serials

 23 Theoretical and Mathematical Physics 19 Journal of Mathematical Physics 14 Physica D 10 Journal of Geometry and Physics 8 Physics Letters. A 7 Nonlinearity 7 Functional Analysis and its Applications 7 Journal of Nonlinear Mathematical Physics 7 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 7 Proceedings of the Steklov Institute of Mathematics 6 Communications in Mathematical Physics 6 Mathematical Notes 6 Siberian Mathematical Journal 6 The Journal of Geometric Analysis 5 Russian Mathematical Surveys 5 Studies in Applied Mathematics 5 Journal of Nonlinear Science 5 Journal of Inverse and Ill-Posed Problems 4 Applicable Analysis 4 Bulletin des Sciences Mathématiques 3 Inverse Problems 3 Letters in Mathematical Physics 3 Duke Mathematical Journal 3 Journal of Differential Equations 3 Journal of Functional Analysis 3 Journal of Soviet Mathematics 3 Programming and Computer Software 3 Communications in Partial Differential Equations 3 Journal of Mathematical Sciences (New York) 3 Mathematical Physics, Analysis and Geometry 2 Journal of Mathematical Analysis and Applications 2 Physics Letters. B 2 Advances in Mathematics 2 Compositio Mathematica 2 Journal für die Reine und Angewandte Mathematik 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Transactions of the American Mathematical Society 2 Regular and Chaotic Dynamics 2 Annales Henri Poincaré 2 Inverse Problems and Imaging 2 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Ukrainian Mathematical Journal 1 Wave Motion 1 Chaos, Solitons and Fractals 1 Applied Mathematics and Computation 1 Inventiones Mathematicae 1 Manuscripta Mathematica 1 Ricerche di Matematica 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 Applied Mathematics Letters 1 International Journal of Mathematics 1 Differential Geometry and its Applications 1 Geometric and Functional Analysis. GAFA 1 Bulletin of the American Mathematical Society. New Series 1 Russian Mathematics 1 Experimental Mathematics 1 Calculus of Variations and Partial Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 Selecta Mathematica. New Series 1 Sbornik: Mathematics 1 Chaos 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Nonlinear Science and Numerical Simulation 1 Lobachevskii Journal of Mathematics 1 Differential Equations 1 Advanced Nonlinear Studies 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of the Institute of Mathematics of Jussieu 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Oberwolfach Reports 1 Journal of Mathematical Physics, Analysis, Geometry 1 Inverse Problems in Science and Engineering 1 Journal of Physics A: Mathematical and Theoretical 1 Advances in Mathematical Physics 1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 1 Séminaire Laurent Schwartz. EDP et Applications
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### Cited in 43 Fields

 155 Partial differential equations (35-XX) 111 Dynamical systems and ergodic theory (37-XX) 49 Quantum theory (81-XX) 30 Algebraic geometry (14-XX) 29 Ordinary differential equations (34-XX) 23 Differential geometry (53-XX) 16 Global analysis, analysis on manifolds (58-XX) 14 Difference and functional equations (39-XX) 14 Operator theory (47-XX) 12 Functions of a complex variable (30-XX) 12 Special functions (33-XX) 11 Numerical analysis (65-XX) 10 Optics, electromagnetic theory (78-XX) 9 Fluid mechanics (76-XX) 6 Commutative algebra (13-XX) 6 Mechanics of particles and systems (70-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Nonassociative rings and algebras (17-XX) 4 Functional analysis (46-XX) 4 Convex and discrete geometry (52-XX) 3 Combinatorics (05-XX) 3 Associative rings and algebras (16-XX) 3 Topological groups, Lie groups (22-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Mechanics of deformable solids (74-XX) 3 Biology and other natural sciences (92-XX) 2 Number theory (11-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Geometry (51-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)

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