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Ablowitz, Mark Jay

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Author ID: ablowitz.mark-j Recent zbMATH articles by "Ablowitz, Mark Jay"
Published as: Ablowitz, M.; Ablowitz, M. J.; Ablowitz, Mark; Ablowitz, Mark J.
External Links: MGP · Wikidata · GND
Documents Indexed: 220 Publications since 1970, including 11 Books
Biographic References: 2 Publications
all top 5

Co-Authors

19 single-authored
21 Fokas, Athanassios S.
18 Herbst, Ben M.
16 Villarroel, Javier
15 Chakravarty, Sarbarish
15 Segur, Harvey
12 Schober, Constance M.
11 Biondini, Gino
11 Musslimani, Ziad H.
10 Prinari, Barbara
9 De Lillo, Silvana
8 Taha, Thiab R.
8 Trubatch, A. David
7 Zhu, Yi
6 Clarkson, Peter A.
6 Halburd, Rodney G.
6 Haut, Terry S.
6 Horikis, Theodoros P.
6 Luo, Xudan
6 Satsuma, Junkichi
5 Newell, Alan C.
5 Santini, Paolo Maria
4 Chakravarty, Sarby
4 Curtis, Christopher W.
4 Kodama, Yuji
4 Ladik, J. F.
4 Nachman, Adrian I.
4 Nixon, Sean D.
3 Feng, Baofeng
3 Kruskal, Martin David
3 Rumanov, Igor
3 Takhtajan, Leon Armenovich
3 Tenenblat, Keti
2 Ahrens, C. D.
2 Askar, Attila
2 Beals, Richard W.
2 Cakmak, Ahmet S.
2 Cole, Justin T.
2 Engin, Hasan
2 Frantzeskakis, Dimitri J.
2 Hammack, Joseph L.
2 Henderson, Diane M.
2 Kaup, David J.
2 Keiser, James M.
2 Ma, Yi-ping
2 Ohta, Yasuhiro
2 Ostrovsky, Lev A.
2 Ramani, Alfred
2 Saridakis, Yiannis G.
2 Schultz, Cherie L.
2 Yang, Jianke
1 Ablowitz, S. A.
1 Airault, Hélène
1 Akylas, T. R.
1 Antar, Nalan
1 Bakirtaş, İlkay
1 Baldwin, Douglas E.
1 Bar Yaacov, D.
1 Barone, Vincenzo
1 Benney, David J.
1 Blair, Steve
1 Boiti, Marco
1 Bona, Jerry Lloyd
1 Chitlaru-Briggs, S.
1 Costa, David Goldstein
1 Degasperis, Antonio
1 Demirci, Ali
1 Docherty, A.
1 Fuchssteiner, Benno
1 Funk, B. A.
1 Hahn, Heekyoung
1 Halburd, Rod
1 Hirooka, Toshihiko
1 Hoefer, Mark A.
1 Ilan, Boaz
1 Ladik, F.
1 Lin, Chia-Chiao
1 Ma, Yan-Chow
1 Mugan, Ugurhan
1 Papadopoulou, Elena P.
1 Papatheodorou, Theodore S.
1 Pempinelli, Flora
1 Ragnisco, Orlando
1 Ryan, E.
1 Sommacal, Matteo
1 Varadi, Ferenc
1 Villorroel, J.
1 Wadati, Miki
1 Wang, Qiao
1 Wang, Xiaoping
1 Wang, Xueping
1 Weideman, J. André C.
1 Zakharov, Victor V.
1 Zeppetella, Anthony
all top 5

Serials

43 Studies in Applied Mathematics
22 Journal of Mathematical Physics
14 Physica D
8 Nonlinearity
7 Journal of Computational Physics
6 SIAM Journal on Applied Mathematics
5 Physics Letters. A
5 Mathematics and Computers in Simulation
5 Journal of Physics A: Mathematical and General
5 Journal of Physics A: Mathematical and Theoretical
4 Physical Review Letters
4 Cambridge Texts in Applied Mathematics
3 Communications in Mathematical Physics
3 Inverse Problems
3 Journal of Fluid Mechanics
3 Theoretical and Mathematical Physics
3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 International Journal of Non-Linear Mechanics
2 Journal of Engineering Mathematics
2 Quaestiones Mathematicae
2 Acta Applicandae Mathematicae
2 Chaos
2 London Mathematical Society Lecture Note Series
1 Computer Physics Communications
1 IMA Journal of Numerical Analysis
1 Bulletin of Mathematical Biology
1 Chaos, Solitons and Fractals
1 Journal of Computational and Applied Mathematics
1 SIAM Journal on Mathematical Analysis
1 SIAM Review
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Matemática Aplicada e Computacional
1 Journal of Nonlinear Science
1 Physics of Fluids
1 The Asian Journal of Mathematics
1 International Journal of Modern Physics C
1 Journal of the Physical Society of Japan
1 Journal of Nonlinear Mathematical Physics
1 Analysis and Applications (Singapore)
1 Dynamics of Partial Differential Equations
1 Lectures in Applied Mathematics
1 SIAM Studies in Applied Mathematics
1 Discrete and Continuous Dynamical Systems. Series S
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences

Publications by Year

Citations contained in zbMATH Open

185 Publications have been cited 8,377 times in 5,596 Documents Cited by Year
Solitons, nonlinear evolution equations and inverse scattering. Zbl 0762.35001
Ablowitz, M. J.; Clarkson, P. A.
1991
Solitons and the inverse scattering transform. Zbl 0472.35002
Ablowitz, Mark J.; Segur, Harvey
1981
The inverse scattering transform-Fourier analysis for nonlinear problems. Zbl 0408.35068
Ablowitz, Mark J.; Kaup, David J.; Newell, Alan C.; Segur, Harvey
629
1974
The inverse scattering transform: Semi-infinite interval. Zbl 0299.35076
Ablowitz, M. J.; Segur, H.
432
1975
A connection between nonlinear evolution equations and ordinary differential equations of P-type. I. Zbl 0445.35056
Ablowitz, M. J.; Ramani, A.; Segur, H.
237
1980
Nonlinear differential-difference equations. Zbl 0296.34062
Ablowitz, M. J.; Ladik, F.
221
1975
Nonlinear-evolution equations of physical significance. Zbl 1243.35143
Ablowitz, Mark J.; Kaup, David J.; Newell, Alan C.; Segur, Harvey
184
1973
Nonlinear differential-difference equations and Fourier analysis. Zbl 0322.42014
Ablowitz, M. J.; Ladik, J. F.
183
1976
Discrete and continuous nonlinear Schrödinger systems. Zbl 1057.35058
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
160
2004
Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation. Zbl 0541.65082
Taha, Thiab R.; Ablowitz, Mark J.
118
1984
On the evolution of packets of water waves. Zbl 0413.76009
Ablowitz, Mark J.; Segur, Harvey
118
1979
Explicit solutions of Fisher’s equation for a special wave speed. Zbl 0423.35079
Ablowitz, Mark J.; Zeppetella, Anthony
115
1979
Two-dimensional lumps in nonlinear dispersive systems. Zbl 0422.35014
Satsuma, J.; Ablowitz, M. J.
113
1979
Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation. Zbl 1338.37099
Ablowitz, Mark J.; Musslimani, Ziad H.
110
2016
Complex variables: introduction and applications. 2nd ed. Zbl 1088.30001
Ablowitz, Mark J.; Fokas, Athanassios S.
108
2003
A nonlinear difference scheme and inverse scattering. Zbl 0338.35002
Ablowitz, M. J.; Ladik, J. F.
108
1976
On the extension of the Painlevé property to difference equations. Zbl 0956.39003
Ablowitz, M. J.; Halburd, R.; Herbst, B.
93
2000
Solitons and rational solutions of nonlinear evolution equations. Zbl 0418.35022
Ablowitz, M. J.; Satsuma, J.
88
1978
Integrable nonlocal nonlinear equations. Zbl 1373.35281
Ablowitz, Mark J.; Musslimani, Ziad H.
85
2017
A connection between nonlinear evolution equations and ordinary differential equations of P-type. II. Zbl 0445.35057
Ablowitz, M. J.; Ramani, A.; Segur, H.
74
1980
The inverse scattering transform for the Benjamin-Ono equation A pivot to multidimensional problems. Zbl 0505.76031
Fokas, A. S.; Ablowitz, M. J.
73
1983
Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation. Zbl 0541.65083
Taha, Thiab R.; Ablowitz, Mark J.
72
1984
On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane. Zbl 0557.35110
Fokas, A. S.; Ablowitz, M. J.
70
1984
On the inverse scattering transform for the Kadomtsev-Petviashvili equation. Zbl 0527.35080
Ablowitz, M. J.; Bar Yaacov, D.; Fokas, A. S.
70
1983
Asymptotic solutions of the Korteweg-deVries equation. Zbl 0369.35055
Ablowitz, M. J.; Segur, H.
69
1977
On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds. Zbl 0866.65064
Ablowitz, M. J.; Herbst, B. M.; Schober, Constance
66
1996
Complex variables: introduction and applications. Zbl 0885.30001
Ablowitz, Mark J.; Fokas, Athanassios S.
61
1997
The periodic cubic Schrödinger equation. Zbl 0493.35032
Ma, Yan-Chow; Ablowitz, Mark J.
59
1981
On a unified approach to transformations and elementary solutions of Painleve equations. Zbl 0504.34022
Fokas, A. S.; Ablowitz, M. J.
53
1982
On the inverse scattering of the time-dependent Schrödinger equation and the associated Kadomtsev-Petviashvili equation. Zbl 0528.35079
Fokas, A. S.; Ablowitz, M. J.
52
1983
Nonlinear dispersive waves. Asymptotic analysis and solitons. Zbl 1232.35002
Ablowitz, Mark J.
51
2011
On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. Zbl 0707.35141
Ablowitz, Mark J.; Herbst, B. M.
51
1990
On the solution of a class of nonlinear partial difference equations. Zbl 0384.35018
Ablowitz, M. J.; Ladik, J. F.
49
1977
On a new non-local formulation of water waves. Zbl 1098.76013
Ablowitz, M. J.; Fokas, A. S.; Musslimani, Z. H.
48
2006
Perturbations of solitons and solitary waves. Zbl 0486.76029
Kodama, Yuji; Ablowitz, Mark J.
47
1981
The evolution of multi-phase modes for nonlinear dispersive waves. Zbl 0203.41001
Ablowitz, M. J.; Benney, D. J.
46
1970
Integrable nonlinear Schrödinger systems and their soliton dynamics. Zbl 1153.35389
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
37
2004
Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions. Zbl 1383.35204
Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.
36
2018
A multidimensional inverse-scattering method. Zbl 0557.35032
Nachman, Adrian I.; Ablowitz, Mark J.
36
1984
A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions. Zbl 0795.58027
Ablowitz, Mark J.; Chakravarty, Sarbarish; Takhtajan, Leon A.
34
1993
Forced nonlinear evolution equations and the inverse scattering transform. Zbl 0696.35135
Fokas, A. S.; Ablowitz, M. J.
34
1989
Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions. Zbl 1112.37070
Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino
33
2006
Solitary wave collisions. Zbl 0408.65075
Ablowitz, M. J.; Kruskal, M. D.; Ladik, J. F.
33
1979
Direct and inverse scattering problems of the nonlinear intermediate long wave equation. Zbl 0489.35004
Kodama, Y.; Ablowitz, M. J.; Satsuma, J.
31
1982
Reductions of self-dual Yang-Mills fields and classical systems. Zbl 1050.81587
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
29
1990
The decay of the continuous spectrum for solutions of the Korteweg-de Vries equation. Zbl 0261.35070
Ablowitz, Mark J.; Newell, Alan C.
28
1973
Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation. Zbl 0824.35116
Wang, X. P.; Ablowitz, M. J.; Segur, H.
27
1994
Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions. Zbl 1127.35059
Ablowitz, Mark J.; Biondini, Gino; Prinari, Barbara
26
2007
On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes. Zbl 0874.65076
Ablowitz, M. J.; Herbst, B. M.; Schober, C. M.
25
1997
Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation. Zbl 0900.65350
Herbst, B. M.; Ablowitz, Mark J.; Ryan, E.
25
1991
Hodograph transformations of linearizable partial differential equations. Zbl 0694.35005
Clarkson, P. A.; Fokas, A. S.; Ablowitz, M. J.
25
1989
Integrable systems and reductions of the self-dual Yang-Mills equations. Zbl 1062.70050
Ablowitz, M. J.; Chakravarty, S.; Halburd, R. G.
24
2003
On the solution of the generalized wave and generalized sine-Gordon equations. Zbl 0626.35082
Ablowitz, Mark J.; Beals, Richard; Tenenblat, Keti
24
1986
Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent. Zbl 1194.35388
Segur, Harvey; Ablowitz, Mark J.
24
1981
Analytical and numerical aspects of certain nonlinear evolution equations. I. Analytical. Zbl 0541.65081
Taha, Thiab R.; Ablowitz, Mark J.
23
1984
Long internal waves in fluids of great depth. Zbl 0447.76013
Ablowitz, M. J.; Segur, H.
20
1980
Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach. Zbl 1030.78007
Ablowitz, Mark J.; Musslimani, Ziad H.
19
2003
Solutions to the time dependent Schrödinger and the Kadomtsev-Petviashvili equations. Zbl 0944.81013
Ablowitz, Mark J.; Villarroel, Javier
19
1997
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.
19
1984
Lectures on the inverse scattering transform. Zbl 0384.35019
Ablowitz, Mark J.
19
1978
General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions. Zbl 1406.37049
Feng, Bao-Feng; Luo, Xu-Dan; Ablowitz, Mark J.; Musslimani, Ziad H.
18
2018
A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations. Zbl 0947.35129
Ablowitz, M. J.; Chakravarty, S.; Trubatch, A. D.; Villarroel, J.
18
2000
On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation. Zbl 0947.35145
Villarroel, Javier; Ablowitz, Mark J.
18
1999
On discretizations of the vector nonlinear Schrödinger equation. Zbl 0938.35174
Ablowitz, Mark J.; Ohta, Yasuhiro; Trubatch, A. David
18
1999
On the initial value problem of the second Painleve transcendent. Zbl 0524.35094
Fokas, A. S.; Ablowitz, M. J.
18
1983
Nonlinear waves in shallow honeycomb lattices. Zbl 1258.41012
Ablowitz, Mark J.; Zhu, Yi
15
2012
Soliton interactions in the vector NLS equation. Zbl 1074.35082
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
15
2004
A method of linearization for Painlevé equations: Painlevé IV, V. Zbl 0649.34006
Fokas, A. S.; Mugan, U.; Ablowitz, M. J.
15
1988
Semi-resonant interactions and frequency dividers. Zbl 0257.70017
Ablowitz, M. J.; Funk, B. A.; Newell, A. C.
15
1973
On the IST for discrete nonlinear Schrödinger systems and polarization shift for discrete vector solitons. Zbl 1053.37053
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
14
2003
Numerical simulation of quasi-periodic solutions of the sine-Gordon equation. Zbl 1194.65121
Ablowitz, Mark J.; Herbst, B. M.; Schober, Constance M.
14
1995
On the Kadomtsev-Petviashvili equation and associated constraints. Zbl 0742.35051
Ablowitz, Mark J.; Villarroel, Javier
14
1991
On the initial value problem for the KP II equation with data that do not decay along a line. Zbl 1082.35137
Villarroel, Javier; Ablowitz, Mark J.
13
2004
Applications of slowly varying nonlinear dispersive wave theories. Zbl 0229.76016
Ablowitz, M. J.
13
1971
Integrable systems and modular forms of level 2. Zbl 1123.37031
Ablowitz, Mark J.; Chakravarty, Sarbarish; Hahn, Heekyoung
12
2006
Long-time dynamics of the modulational instability of deep water waves. Zbl 1049.76005
Ablowitz, M. J.; Hammack, J.; Henderson, D.; Schober, C. M.
12
2001
The generalized Chazy equation from the self-duality equations. Zbl 1136.34301
Ablowitz, M. J.; Chakravarty, S.; Halburd, R.
12
1999
A new Hamiltonian amplitude equation governing modulated wave instabilities. Zbl 1112.35354
Wadati, Miki; Segur, H.; Ablowitz, M. J.
12
1992
Approximate methods for obtaining multi-phase modes in nonlinear dispersive wave problems. Zbl 0261.76010
Ablowitz, M. J.
12
1972
Symplectic methods for the nonlinear Schrödinger equation. Zbl 0812.65118
Herbst, B. M.; Varadi, F.; Ablowitz, M. J.
11
1994
Numerical homoclinic instabilities in the sine-Gordon equation. Zbl 0785.65086
Herbst, B. M.; Ablowitz, M. J.
11
1992
Multidimensional nonlinear evolution equations and inverse scattering. Zbl 0604.35070
Ablowitz, Mark J.; Nachman, Adrian I.
11
1986
Nonlinear evolution equations - continuous and discrete. Zbl 0375.35030
Ablowitz, Mark J.
11
1977
Inverse scattering transform for the nonlocal reverse space-time nonlinear Schrödinger equation. Zbl 1408.35169
Ablowitz, M. J.; Feng, Bao-Feng; Luo, Xu-Dan; Musslimani, Z. H.
10
2018
Interacting nonlinear wave envelopes and rogue wave formation in deep water. Zbl 1326.76015
Ablowitz, Mark J.; Horikis, Theodoros P.
10
2015
On tight-binding approximations in optical lattices. Zbl 1297.35212
Ablowitz, Mark J.; Curtis, Christopher W.; Zhu, Yi
10
2012
On a Burgers-Stefan problem. Zbl 0943.35109
Ablowitz, M. J.; De Lillo, S.
10
2000
Solitons and symmetries. Zbl 0932.35174
Ablowitz, M. J.; Clarkson, P. A.
10
1999
Analytical and numerical aspects of certain nonlinear evolution equations. IV: Numerical, modified Korteweg-de Vries equation. Zbl 0646.65087
Taha, Thiab R.; Ablowitz, Mark J.
10
1988
Topics in soliton theory and exactly solvable nonlinear equations. Proceedings of the conference on nonlinear evolution equations, solitons and the inverse scattering transform, Oberwolfach, Germany, July 27- August 2, 1986. Zbl 0721.00016
Ablowitz, M. (ed.); Fuchssteiner, B. (ed.); Kruskal, M. (ed.)
10
1987
Multidimensional inverse scattering for first-order systems. Zbl 0557.35121
Nachman, Adrian I.; Ablowitz, Mark J.
10
1984
A note on Miura’s transformation. Zbl 0425.35005
Ablowitz, Mark J.; Kruskal, Martin; Segur, Harvey
10
1979
Reverse space-time nonlocal sine-Gordon/sinh-Gordon equations with nonzero boundary conditions. Zbl 1420.35304
Ablowitz, Mark J.; Feng, Bao-Feng; Luo, Xu-Dan; Musslimani, Ziad H.
9
2018
Parameterizations of the Chazy equation. Zbl 1217.34136
Chakravarty, Sarbarish; Ablowitz, Mark J.
9
2010
A reformulation and applications of interfacial fluids with a free surface. Zbl 1181.76042
Haut, T. S.; Ablowitz, M. J.
9
2009
Interactions of dispersive shock waves. Zbl 1131.35077
Hoefer, M. A.; Ablowitz, M. J.
9
2007
The generalized Chazy equation and Schwarzian triangle functions. Zbl 0969.34005
Ablowitz, M. J.; Chakravarty, S.; Halburd, R.
9
1998
On a Bäcklund transformation and scattering problem for the modified intermediate long wave equation. Zbl 0583.76021
Satsuma, Junkichi; Taha, Thiab R.; Ablowitz, Mark J.
9
1984
The direct linearization of a class of nonlinear evolution equations. Zbl 0557.35111
Santini, P. M.; Ablowitz, M. J.; Fokas, A. S.
9
1984
The inverse scattering transform for multidimensional (2+1) problems. Zbl 0528.35078
Fokas, Athanassios S.; Ablowitz, Mark J.
9
1983
On the Whitham system for the radial nonlinear Schrödinger equation. Zbl 1418.35332
Ablowitz, Mark J.; Cole, Justin T.; Rumanov, Igor
2
2019
Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions. Zbl 1383.35204
Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.
36
2018
General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions. Zbl 1406.37049
Feng, Bao-Feng; Luo, Xu-Dan; Ablowitz, Mark J.; Musslimani, Ziad H.
18
2018
Inverse scattering transform for the nonlocal reverse space-time nonlinear Schrödinger equation. Zbl 1408.35169
Ablowitz, M. J.; Feng, Bao-Feng; Luo, Xu-Dan; Musslimani, Z. H.
10
2018
Reverse space-time nonlocal sine-Gordon/sinh-Gordon equations with nonzero boundary conditions. Zbl 1420.35304
Ablowitz, Mark J.; Feng, Bao-Feng; Luo, Xu-Dan; Musslimani, Ziad H.
9
2018
Whitham modulation theory for \((2+1)\)-dimensional equations of Kadomtsev-Petviashvili type. Zbl 1397.37069
Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor
3
2018
Solitons, the Korteweg-de Vries equation with step boundary values, and pseudo-embedded eigenvalues. Zbl 1410.35163
Ablowitz, M. J.; Luo, X.-D.; Cole, J. T.
2
2018
Integrable nonlocal nonlinear equations. Zbl 1373.35281
Ablowitz, Mark J.; Musslimani, Ziad H.
85
2017
Whitham modulation theory for the Kadomtsev-Petviashvili equation. Zbl 1404.35382
Ablowitz, Mark J.; Biondini, Gino; Wang, Qiao
4
2017
Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation. Zbl 1338.37099
Ablowitz, Mark J.; Musslimani, Ziad H.
110
2016
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations. Zbl 1415.35237
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
6
2016
Interacting nonlinear wave envelopes and rogue wave formation in deep water. Zbl 1326.76015
Ablowitz, Mark J.; Horikis, Theodoros P.
10
2015
Inverse scattering transform for 3-level coupled Maxwell-Bloch equations with inhomogeneous broadening. Zbl 1349.35261
Chakravarty, S.; Prinari, B.; Ablowitz, M. J.
6
2014
On the existence of real spectra in \(\mathcal {PT}\)-symmetric honeycomb optical lattices. Zbl 1291.81151
Curtis, Christopher W.; Ablowitz, Mark J.
3
2014
Nonlinear wave packets in deformed honeycomb lattices. Zbl 1295.41030
Ablowitz, Mark J.; Zhu, Yi
6
2013
Conservation laws and non-decaying solutions for the Benney-Luke equation. Zbl 1320.76018
Ablowitz, Mark J.; Curtis, Christopher W.
5
2013
Interactions and asymptotics of dispersive shock waves – Korteweg-de Vries equation. Zbl 1428.35441
Ablowitz, Mark J.; Baldwin, Douglas E.
2
2013
Dark solitons of the power-energy saturation model: application to mode-locked lasers. Zbl 1272.78021
Ablowitz, M. J.; Nixon, S. D.; Horikis, T. P.; Frantzeskakis, D. J.
1
2013
Nonlinear waves in shallow honeycomb lattices. Zbl 1258.41012
Ablowitz, Mark J.; Zhu, Yi
15
2012
On tight-binding approximations in optical lattices. Zbl 1297.35212
Ablowitz, Mark J.; Curtis, Christopher W.; Zhu, Yi
10
2012
Nonlinear dispersive waves. Asymptotic analysis and solitons. Zbl 1232.35002
Ablowitz, Mark J.
51
2011
Perturbations of dark solitons. Zbl 1228.35213
Ablowitz, M. J.; Nixon, S. D.; Horikis, T. P.; Frantzeskakis, D. J.
4
2011
On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation. Zbl 1432.76066
Ablowitz, Mark J.; Curtis, Christopher W.
2
2011
Parameterizations of the Chazy equation. Zbl 1217.34136
Chakravarty, Sarbarish; Ablowitz, Mark J.
9
2010
Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions. Zbl 1378.76017
Ablowitz, M. J.; Haut, T. S.
1
2010
A reformulation and applications of interfacial fluids with a free surface. Zbl 1181.76042
Haut, T. S.; Ablowitz, M. J.
9
2009
Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions. Zbl 1186.35151
Ablowitz, M. J.; Haut, T. S.
2
2009
Coupled nonlinear Schrödinger equations for interfacial fluids with a free surface. Zbl 1278.76013
Ablowitz, M. J.; Haut, T. S.
2
2009
Asymptotic analysis of pulse dynamics in mode-locked lasers. Zbl 1175.37072
Ablowitz, Mark J.; Horikis, Theodoros P.; Nixon, Sean D.; Zhu, Yi
2
2009
Spectral formulation of the two-fluid Euler equations with a free interface and long-wave reductions. Zbl 1154.76015
Ablowitz, M. J.; Haut, T. S.
5
2008
Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions. Zbl 1127.35059
Ablowitz, Mark J.; Biondini, Gino; Prinari, Barbara
26
2007
Interactions of dispersive shock waves. Zbl 1131.35077
Hoefer, M. A.; Ablowitz, M. J.
9
2007
On a new non-local formulation of water waves. Zbl 1098.76013
Ablowitz, M. J.; Fokas, A. S.; Musslimani, Z. H.
48
2006
Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions. Zbl 1112.37070
Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino
33
2006
Integrable systems and modular forms of level 2. Zbl 1123.37031
Ablowitz, Mark J.; Chakravarty, Sarbarish; Hahn, Heekyoung
12
2006
Discrete vector solitons: Composite solitons, Yang-Baxter maps and computation. Zbl 1145.37332
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
1
2006
Wave collapse in a class of nonlocal nonlinear Schrödinger equations. Zbl 1080.35132
Ablowitz, Mark; Bakırtaş, İlkay; Ilan, Boaz
6
2005
Solvability of the direct and inverse problems for the nonlinear Schrödinger equation. Zbl 1084.34009
Villarroel, Javier; Ablowitz, Mark J.; Prinari, Barbara
6
2005
On a “quasi” integrable discrete Eckhaus equation. Zbl 1362.39004
Ablowitz, M. J.; Ahrens, C. D.; De Lillo, S.
1
2005
Periodic-group-delay dispersion compensation reduces collision-induced timing shifts in dispersion-managed quasilinear systems. Zbl 1178.35341
Ablowitz, M. J.; Ahrens, C.; Biondini, G.; Chakravarty, S.; Docherty, A.
1
2005
Discrete and continuous nonlinear Schrödinger systems. Zbl 1057.35058
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
160
2004
Integrable nonlinear Schrödinger systems and their soliton dynamics. Zbl 1153.35389
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
37
2004
Soliton interactions in the vector NLS equation. Zbl 1074.35082
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
15
2004
On the initial value problem for the KP II equation with data that do not decay along a line. Zbl 1082.35137
Villarroel, Javier; Ablowitz, Mark J.
13
2004
Initial value problems and solutions of the Kadomtsev-Petviashvili equation. Zbl 1064.35160
Ablowitz, M. J.; Villarroel, J.
2
2004
Complex variables: introduction and applications. 2nd ed. Zbl 1088.30001
Ablowitz, Mark J.; Fokas, Athanassios S.
108
2003
Integrable systems and reductions of the self-dual Yang-Mills equations. Zbl 1062.70050
Ablowitz, M. J.; Chakravarty, S.; Halburd, R. G.
24
2003
Discrete spatial solitons in a diffraction-managed nonlinear waveguide array: a unified approach. Zbl 1030.78007
Ablowitz, Mark J.; Musslimani, Ziad H.
19
2003
On the IST for discrete nonlinear Schrödinger systems and polarization shift for discrete vector solitons. Zbl 1053.37053
Ablowitz, M. J.; Prinari, B.; Trubatch, A. D.
14
2003
On the discrete spectrum of systems in the plane and the Davey–Stewartson II equation. Zbl 1044.35096
Villarroel, Javier; Ablowitz, Mark J.
3
2003
Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 – July 6, 2002. Zbl 1051.81500
Ablowitz, M. J. (ed.); Boiti, M. (ed.); Pempinelli, F. (ed.); Prinari, B. (ed.)
1
2003
On a two-phase boundary problem. Zbl 1168.76380
Ablowitz, M. J.; De Lillo, S.
1
2003
The Cauchy problem for the Kadomtsev-Petviashvili II equation with nondecaying data along a line. Zbl 1152.35480
Villarroel, J.; Ablowitz, M. J.
8
2002
Long-time dynamics of the modulational instability of deep water waves. Zbl 1049.76005
Ablowitz, M. J.; Hammack, J.; Henderson, D.; Schober, C. M.
12
2001
Discretizations, integrable systems and computation. Zbl 0991.65137
Ablowitz, M. J.; Herbst, B. M.; Schober, C. M.
8
2001
Localized multi-dimensional optical pulses in non-resonant quadratic materials. Zbl 0972.78017
Ablowitz, Mark J.; Biondini, Gino; Blair, Steve
1
2001
On the extension of the Painlevé property to difference equations. Zbl 0956.39003
Ablowitz, M. J.; Halburd, R.; Herbst, B.
93
2000
A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations. Zbl 0947.35129
Ablowitz, M. J.; Chakravarty, S.; Trubatch, A. D.; Villarroel, J.
18
2000
On a Burgers-Stefan problem. Zbl 0943.35109
Ablowitz, M. J.; De Lillo, S.
10
2000
Optical solitons: perspectives and applications. Zbl 0971.78015
Ablowitz, Mark J.; Biondini, Gino; Ostrovsky, Lev A.
7
2000
Chaotic dynamics of deep water gravity waves. Zbl 0986.76008
Ablowitz, M. J.; Hammack, J.; Henderson, D.; Schober, C. M.
7
2000
Solutions of a Burgers-Stefan problem. Zbl 1115.35372
Ablowitz, M. J.; De Lillo, S.
5
2000
On integrability and chaos in discrete systems. Zbl 1160.37413
Ablowitz, Mark J.; Ohta, Yasuhiro; Trubatch, A. David
5
2000
Optical solitons: perspectives and applications. Zbl 0972.00024
Ablowitz, Mark J. (ed.); Biondini, Gino (ed.); Ostrovsky, L. A. (ed.)
3
2000
On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation. Zbl 0947.35145
Villarroel, Javier; Ablowitz, Mark J.
18
1999
On discretizations of the vector nonlinear Schrödinger equation. Zbl 0938.35174
Ablowitz, Mark J.; Ohta, Yasuhiro; Trubatch, A. David
18
1999
The generalized Chazy equation from the self-duality equations. Zbl 1136.34301
Ablowitz, M. J.; Chakravarty, S.; Halburd, R.
12
1999
Solitons and symmetries. Zbl 0932.35174
Ablowitz, M. J.; Clarkson, P. A.
10
1999
On Painlevé and Darboux-Halphen-type equations. Zbl 1029.34085
Ablowitz, Mark J.; Chakravarty, Sarby; Halburd, Rod
1
1999
The generalized Chazy equation and Schwarzian triangle functions. Zbl 0969.34005
Ablowitz, M. J.; Chakravarty, S.; Halburd, R.
9
1998
The Darboux-Halphen system and the singularity structure of its solutions. Zbl 1051.34500
Ablowitz, M. J.; Chakravarty, S.; Halburd, R.
2
1998
Complex variables: introduction and applications. Zbl 0885.30001
Ablowitz, Mark J.; Fokas, Athanassios S.
61
1997
On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes. Zbl 0874.65076
Ablowitz, M. J.; Herbst, B. M.; Schober, C. M.
25
1997
Solutions to the time dependent Schrödinger and the Kadomtsev-Petviashvili equations. Zbl 0944.81013
Ablowitz, Mark J.; Villarroel, Javier
19
1997
Initial time layers and Kadomtsev-Petviashvili-type equations. Zbl 0879.35132
Ablowitz, Mark J.; Wang, Xiao-Ping
5
1997
The nonlinear Schrödinger equation: Asymmetric perturbations, traveling waves and chaotic structures. Zbl 0869.68125
Ablowitz, M. J.; Herbst, B. M.; Schober, C. M.
5
1997
On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds. Zbl 0866.65064
Ablowitz, M. J.; Herbst, B. M.; Schober, Constance
66
1996
Integrability, monodromy evolving deformations, and self-dual Bianchi IX systems. Zbl 0955.83502
Chakravarty, S.; Ablowitz, M. J.
7
1996
The Burgers equation under deterministic and stochastic forcing. Zbl 0900.76482
Ablowitz, M. J.; De Lillo, S.
7
1996
On a \(2+1\) Volterra system. Zbl 0897.35071
Villarroel, Javier; Chakravarty, Sarbarish; Ablowitz, Mark J.
5
1996
On the numerics of integrable discretizations. Zbl 0856.65107
Ablowitz, M. J.; Herbst, B. M.; Schober, C.
2
1996
Numerical simulation of quasi-periodic solutions of the sine-Gordon equation. Zbl 1194.65121
Ablowitz, Mark J.; Herbst, B. M.; Schober, Constance M.
14
1995
Integrability, computation and applications. Zbl 0832.58019
Ablowitz, M. J.; Chakravarty, S.; Herbst, B. M.
2
1995
Numerical stochasticity, Hamiltonian integrators, and the nonlinear Schrödinger equation. Zbl 0929.35141
Ablowitz, Mark J.; Schober, Constance
1
1995
Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation. Zbl 0824.35116
Wang, X. P.; Ablowitz, M. J.; Segur, H.
27
1994
Symplectic methods for the nonlinear Schrödinger equation. Zbl 0812.65118
Herbst, B. M.; Varadi, F.; Ablowitz, M. J.
11
1994
Effective chaos in the nonlinear Schrödinger equation. Zbl 0807.35131
Ablowitz, M. J.; Schober, C. M.
7
1994
Hamiltonian integrators for the nonlinear Schrödinger equation. Zbl 0940.65518
Ablowitz, Mark J.; Schober, Constance M.
4
1994
Parametric forcing, bound states and solutions of a nonlinear Schrödinger type equation. Zbl 0809.35122
Ablowitz, M. J.; De Lillo, S.
3
1994
Homoclinic manifolds and numerical chaos in the nonlinear Schrödinger equation. Zbl 0811.65118
Ablowitz, Mark J.; Schober, Constance M.
1
1994
Solutions to the \(2+1\) Toda equation. Zbl 0812.35132
Villarroel, Javier; Ablowitz, Mark J.
1
1994
A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions. Zbl 0795.58027
Ablowitz, Mark J.; Chakravarty, Sarbarish; Takhtajan, Leon A.
34
1993
On the inverse scattering transform of the 2+1 Toda equation. Zbl 0771.35065
Villarroel, Javier; Ablowitz, Mark J.
6
1993
Numerical chaos, symplectic integrators, and exponentially small splitting distances. Zbl 0772.65084
Herbst, B. M.; Ablowitz, Mark J.
6
1993
Rapidly forced Burgers equation. Zbl 0793.35087
Ablowitz, M. J.; de Lillo, S.
3
1993
On the elliptic \(2+1\) Toda equation. Zbl 0786.35117
Villarroel, J.; Ablowitz, M. J.
1
1993
A new Hamiltonian amplitude equation governing modulated wave instabilities. Zbl 1112.35354
Wadati, Miki; Segur, H.; Ablowitz, M. J.
12
1992
Numerical homoclinic instabilities in the sine-Gordon equation. Zbl 0785.65086
Herbst, B. M.; Ablowitz, M. J.
11
1992
Self-dual Yang-Mills equation and new special functions in integrable systems. Zbl 0941.37542
Chakravarty, S.; Ablowitz, M. J.; Takhtajan, L. A.
4
1992
On reductions of self-dual Yang-Mills equations. Zbl 0875.35079
Chakravarty, S.; Ablowitz, Mark J.
2
1992
...and 85 more Documents
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Cited by 5,230 Authors

121 Ma, Wen-Xiu
97 Zhang, Hongqing
95 Ablowitz, Mark Jay
69 Geng, Xianguo
62 Tian, Bo
62 Wazwaz, Abdul-Majid Abdul-Rahman
59 Yan, Zhenya
57 Fokas, Athanassios S.
49 Kudryashov, Nikolaĭ Alekseevich
45 Tian, Shoufu
43 Gao, Yitian
40 Chen, Yong
38 Zhang, Yufeng
35 Biswas, Anjan
35 Zhang, Sheng
34 Clarkson, Peter A.
34 Xia, Tie-Cheng
34 Zhang, Tiantian
33 Bekir, Ahmet
33 Biondini, Gino
32 He, Jingsong
32 Lou, Senyue
32 Xu, Xixiang
30 Chen, Dengyuan
30 Santini, Paolo Maria
30 Zhang, Dajun
29 Pelinovsky, Dmitry Efimovich
29 Wen, Xiaoyong
28 Fan, Engui
28 Grammaticos, Basil
28 Lü, Xing
28 Ramani, Alfred
27 Dai, Zhengde
27 Sahadevan, Ramajayam
26 Wang, Dengshan
25 Deconinck, Bernard
25 Grimshaw, Roger Hamilton James
25 Kevrekidis, Panayotis G.
25 Yu, Fajun
24 Chen, Zongxuan
24 Van der Mee, Cornelis Victor Maria
23 Khalique, Chaudry Masood
23 Konopelchenko, Boris Georgievich
23 Wang, Qi
23 Winternitz, Pavel
22 Lakshmanan, Muthusamy
21 Qiao, Zhijun
21 Sakhnovich, Alexander L.
20 Gerdzhikov, Vladimir Stefanov
20 Its, Alexander Rudolfovich
20 Li, Biao
20 Wang, Xiubin
19 Boiti, Marco
19 Bratsos, Athanassios G.
19 Pempinelli, Flora
19 Prinari, Barbara
19 Segur, Harvey
19 Yu, Xin
18 Zayed, Elsayed M. E.
17 Rogers, Colin
17 Schober, Constance M.
17 Shen, Shoufeng
17 Zhu, Zuonong
16 Chow, Kwok Wing
16 Dong, Huanhe
16 Kaup, David J.
16 Korhonen, Risto
16 Song, Lina
16 Tenenblat, Keti
16 Xue, Bo
16 Yang, Hongxiang
16 Zhang, Haiqiang
15 De Lillo, Silvana
15 Demontis, Francesco
15 Guha, Partha
15 Malomed, Boris A.
15 Mihalache, Dumitru
15 Pickering, Andrew
15 Saut, Jean-Claude
15 Yang, Jianke
14 Bao, Weizhu
14 Feng, Zhaosheng
14 Fuchssteiner, Benno
14 Gordoa, Pilar Ruiz
14 He, Guoliang
14 Osborne, Alfred R.
14 Sun, Yepeng
14 Taha, Thiab R.
14 Yusufoğlu (Agadjanov), Elçin
14 Zeng, Xin
14 Zhang, Yi
13 Gürses, Metin
13 Inc, Mustafa
13 Li, Jibin
13 Meng, Xianghua
13 Pogrebkov, Andrei K.
13 Stepanyants, Yury A.
13 Vakhnenko, Oleksiy O.
13 Xu, Guiqiong
13 Xu, Tao
...and 5,130 more Authors
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Cited in 388 Serials

496 Journal of Mathematical Physics
384 Applied Mathematics and Computation
327 Chaos, Solitons and Fractals
279 Physics Letters. A
251 Physica D
181 Communications in Nonlinear Science and Numerical Simulation
159 Studies in Applied Mathematics
131 Nonlinear Dynamics
123 Theoretical and Mathematical Physics
122 Computers & Mathematics with Applications
119 Applied Mathematics Letters
117 Journal of Mathematical Analysis and Applications
91 Communications in Mathematical Physics
85 Journal of Nonlinear Mathematical Physics
74 Wave Motion
71 Mathematics and Computers in Simulation
66 Journal of Fluid Mechanics
62 Journal of Differential Equations
57 Journal of Computational Physics
51 Chaos
49 Journal of Computational and Applied Mathematics
48 Letters in Mathematical Physics
48 Abstract and Applied Analysis
47 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
43 Acta Applicandae Mathematicae
42 International Journal of Modern Physics B
42 International Journal of Theoretical Physics
41 Journal of Geometry and Physics
41 Advances in Difference Equations
32 Reports on Mathematical Physics
32 Advances in Mathematical Physics
31 Mathematical Problems in Engineering
30 Journal of Nonlinear Science
29 Physica A
28 Computer Physics Communications
27 Nonlinearity
26 Mathematical Methods in the Applied Sciences
26 Mathematical and Computer Modelling
26 Journal of Physics A: Mathematical and Theoretical
24 Annals of Physics
24 Communications in Theoretical Physics
23 Communications on Pure and Applied Mathematics
23 Applied Mathematics and Mechanics. (English Edition)
23 Journal of Applied Mathematics
22 Applied Numerical Mathematics
22 Acta Mathematicae Applicatae Sinica. English Series
22 International Journal of Computer Mathematics
21 ZAMP. Zeitschrift für angewandte Mathematik und Physik
21 Numerical Methods for Partial Differential Equations
20 Modern Physics Letters B
20 Nuclear Physics. B
20 Physical Review Letters
19 Journal of Functional Analysis
19 Journal of Soviet Mathematics
19 Transactions of the American Mathematical Society
19 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
18 Applicable Analysis
18 Complexity
18 Nonlinear Analysis. Real World Applications
17 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
16 Functional Analysis and its Applications
16 Proceedings of the American Mathematical Society
16 Analysis and Mathematical Physics
15 SIAM Journal on Mathematical Analysis
15 Journal of the Egyptian Mathematical Society
15 European Journal of Mechanics. B. Fluids
15 International Journal of Geometric Methods in Modern Physics
15 East Asian Journal on Applied Mathematics
14 Archive for Rational Mechanics and Analysis
14 Advances in Mathematics
14 Journal of Mathematical Sciences (New York)
13 Regular and Chaotic Dynamics
13 Differential Equations
12 Physics of Fluids
12 Numerical Algorithms
12 Journal of High Energy Physics
12 Frontiers of Mathematics in China
11 International Journal of Modern Physics A
11 Reviews in Mathematical Physics
11 Numerische Mathematik
11 Quarterly of Applied Mathematics
11 Discrete and Continuous Dynamical Systems
11 International Journal of Nonlinear Sciences and Numerical Simulation
11 Journal of Applied Analysis and Computation
11 International Journal of Applied and Computational Mathematics
10 International Journal of Engineering Science
10 Ukrainian Mathematical Journal
10 Duke Mathematical Journal
10 Bulletin of the American Mathematical Society. New Series
10 Journal of Shanghai University
10 Discrete and Continuous Dynamical Systems. Series S
9 Fluid Dynamics
9 Journal of Statistical Physics
9 Mathematical Notes
9 Ricerche di Matematica
9 Journal of Scientific Computing
9 Communications in Partial Differential Equations
9 Physics of Fluids
9 Discrete Dynamics in Nature and Society
9 Computational Methods and Function Theory
...and 288 more Serials
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Cited in 60 Fields

4,113 Partial differential equations (35-XX)
2,005 Dynamical systems and ergodic theory (37-XX)
701 Numerical analysis (65-XX)
634 Fluid mechanics (76-XX)
500 Ordinary differential equations (34-XX)
415 Quantum theory (81-XX)
230 Difference and functional equations (39-XX)
191 Statistical mechanics, structure of matter (82-XX)
181 Optics, electromagnetic theory (78-XX)
162 Global analysis, analysis on manifolds (58-XX)
150 Computer science (68-XX)
133 Differential geometry (53-XX)
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121 Mechanics of particles and systems (70-XX)
116 Special functions (33-XX)
106 Mechanics of deformable solids (74-XX)
103 Operator theory (47-XX)
79 Algebraic geometry (14-XX)
71 Nonassociative rings and algebras (17-XX)
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59 Geophysics (86-XX)
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55 Biology and other natural sciences (92-XX)
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