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A semidiscrete Gardner equation |
Haiqiong ZHAO1, Zuonong ZHU2( ) |
| 1. Business Information Management School, Shanghai University of International Business and Economics, Shanghai 201620, China; 2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China |
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Abstract We construct the Darboux transformations, exact solutions, and infinite number of conservation laws for a semidiscrete Gardner equation. A special class of solutions of the semidiscrete equation, called table-top solitons, are given. The dynamical properties of these solutions are also discussed.
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Semidiscrete Gardner equation
Darboux transformation
exact solution
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Corresponding Author(s):
ZHU Zuonong,Email:znzhu@sjtu.edu.cn
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Issue Date: 01 October 2013
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| 1 |
Ablowitz M J, Kaup D J, Newell A C, Segur H. The inverse scattering transform-Fourier analysis for nonlinear problems. Stud Appl Math , 1974, 53: 249-315
|
| 2 |
Ablowitz M J, Ladik J. Nonlinear differential-difference equations. J Math Phys , 1975, 16: 598-603
doi: 10.1063/1.522558
|
| 3 |
Ablowitz M J, Ladik J. Nonlinear differential-difference equations and Fourier analysis. J Math Phys , 1976, 17: 1011-1018
doi: 10.1063/1.523009
|
| 4 |
Ablowitz M J, Segur H. Solitons and the Inverse Scattering Transform. Philadelphia: SIAM , 1981
doi: 10.1137/1.9781611970883
|
| 5 |
Chen Y Z, Liu P L F. On interfacial waves over random topography. Wave Motion , 1996, 24: 169-184
doi: 10.1016/0165-2125(96)00014-5
|
| 6 |
Geng X G. Darboux transformation of the discrete Ablowitz-Ladik eigenvalue problem. Acta Math Sci , 1989, 9: 21-26
|
| 7 |
Grimshaw R, Pelinovsky D, Pelinovsky E, Slunyaev A. Generation of large-amplitude solitons in the extended Korteweg-de Vries equation. Chaos , 2002, 12: 1070-1076
doi: 10.1063/1.1521391
|
| 8 |
Grimshaw R, Slunyaev A, Pelinovsky E. Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity. Chaos , 2010, 20: 013102
doi: 10.1063/1.3279480
|
| 9 |
Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys Rev Lett , 1971, 27: 1192-1194
doi: 10.1103/PhysRevLett.27.1192
|
| 10 |
Hirota R. Exact solution of the modified Korteweg-de Vries equation for multiple collisions of solitons. J Phys Soc Jpn , 1972, 33: 1456-1458
doi: 10.1143/JPSJ.33.1456
|
| 11 |
Hirota R. Exact solution of the sine-Gordon equation for multiple collisions of solitons. J Phys Soc Jpn , 1972, 33: 1459-1463
doi: 10.1143/JPSJ.33.1459
|
| 12 |
Holloway P E, Pelinovsky P E, Talipova T, Barnes B. A nonlinear model of internal tide transformation on the Australian North West Shelf. J Phys Oceanogr , 1997, 27: 871-896
doi: 10.1175/1520-0485(1997)027<0871:ANMOIT>2.0.CO;2
|
| 13 |
Kakutani T, Yamasaki N. Solitary waves on a two-layer fluid. J Phys Soc Jpn , 1978, 45: 674-679
doi: 10.1143/JPSJ.45.674
|
| 14 |
Kodama Y J, Wadati M. Wave propagation in nonlinear lattice III. J Phys Soc Jpn , 1976, 41: 1499-1504
doi: 10.1143/JPSJ.41.1499
|
| 15 |
Malomed B A, Stepanyants Y A. The inverse problem for the Gross-Pitaevskii equation. Chaos , 2010, 20: 013130
doi: 10.1063/1.3367776
|
| 16 |
Miura R M, Gardner C S, Kruskal M D. Korteweg-de Vries equation and generalizations II. Existence of conservation laws and constants of motion. J Math Phys , 1968, 9: 1204-1209
doi: 10.1063/1.1664701
|
| 17 |
Slyunyaev A V. Dynamics of localized waves with large amplitude in a weakly dispersive medium with a quadratic and positive cubic nonlinearity. JETP , 2001, 92: 529-534
doi: 10.1134/1.1364750
|
| 18 |
Slyunyaev A V, Pelinovski E N. Dynamics of large-amplitude solitons. JETP, 1999, 89: 173-181
doi: 10.1134/1.558966
|
| 19 |
Taha T R. A differential-difference equation for a KdV-MKdV equation. Math Comput Simulation , 1993, 35: 509-512
doi: 10.1016/0378-4754(93)90069-7
|
| 20 |
Vekslerchik V E. Implementation of the B?cklund transformations for the Ablowitz-Ladik hierarchy. J Phys A: Math Gen , 2006, 39: 6933-6953
doi: 10.1088/0305-4470/39/22/009
|
| 21 |
Wadati M. Wave propagation in nonlinear lattice I. J Phys Soc Jpn , 1975, 38: 673-680
doi: 10.1143/JPSJ.38.673
|
| 22 |
Wadati M. Wave propagation in nonlinear lattice II. J Phys Soc Jpn , 1975, 38: 681-686
doi: 10.1143/JPSJ.38.681
|
| 23 |
Wadati M, Watanabe M. Conservation laws of a Volterra system and nonlinear selfdual network equation. Prog Theor Phys , 1977, 57: 808-811
doi: 10.1143/PTP.57.808
|
| 24 |
Watanabe S. Ion acoustic soliton in plasma with negative ion. J Phys Soc Jpn , 1984, 53: 950-956
doi: 10.1143/JPSJ.53.950
|
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