Frontiers of Mathematics in China >
A semidiscrete Gardner equation
Received date: 03 Jan 2013
Accepted date: 04 Apr 2013
Published date: 01 Oct 2013
Copyright
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.
Haiqiong ZHAO , Zuonong ZHU . A semidiscrete Gardner equation[J]. Frontiers of Mathematics in China, 2013 , 8(5) : 1099 -1115 . DOI: 10.1007/s11464-013-0309-7
| 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
|
| 3 |
Ablowitz M J, Ladik J. Nonlinear differential-difference equations and Fourier analysis. J Math Phys, 1976, 17: 1011-1018
|
| 4 |
Ablowitz M J, Segur H. Solitons and the Inverse Scattering Transform. Philadelphia: SIAM, 1981
|
| 5 |
Chen Y Z, Liu P L F. On interfacial waves over random topography. Wave Motion, 1996, 24: 169-184
|
| 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
|
| 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
|
| 9 |
Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys Rev Lett, 1971, 27: 1192-1194
|
| 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
|
| 11 |
Hirota R. Exact solution of the sine-Gordon equation for multiple collisions of solitons. J Phys Soc Jpn, 1972, 33: 1459-1463
|
| 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
|
| 13 |
Kakutani T, Yamasaki N. Solitary waves on a two-layer fluid. J Phys Soc Jpn, 1978, 45: 674-679
|
| 14 |
Kodama Y J, Wadati M. Wave propagation in nonlinear lattice III. J Phys Soc Jpn, 1976, 41: 1499-1504
|
| 15 |
Malomed B A, Stepanyants Y A. The inverse problem for the Gross-Pitaevskii equation. Chaos, 2010, 20: 013130
|
| 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
|
| 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
|
| 18 |
Slyunyaev A V, Pelinovski E N. Dynamics of large-amplitude solitons. JETP, 1999, 89: 173-181
|
| 19 |
Taha T R. A differential-difference equation for a KdV-MKdV equation. Math Comput Simulation, 1993, 35: 509-512
|
| 20 |
Vekslerchik V E. Implementation of the Bäcklund transformations for the Ablowitz-Ladik hierarchy. J Phys A: Math Gen, 2006, 39: 6933-6953
|
| 21 |
Wadati M. Wave propagation in nonlinear lattice I. J Phys Soc Jpn, 1975, 38: 673-680
|
| 22 |
Wadati M. Wave propagation in nonlinear lattice II. J Phys Soc Jpn, 1975, 38: 681-686
|
| 23 |
Wadati M, Watanabe M. Conservation laws of a Volterra system and nonlinear selfdual network equation. Prog Theor Phys, 1977, 57: 808-811
|
| 24 |
Watanabe S. Ion acoustic soliton in plasma with negative ion. J Phys Soc Jpn, 1984, 53: 950-956
|
/
| 〈 |
|
〉 |