Citation: | ZHAO Qian, BAI Xi-rui. Two-mode coupled KdV equation: Multiple-soliton solutions and other exact solutions[J]. Journal of East China Normal University (Natural Sciences), 2019, (4): 42-51. doi: 10.3969/j.issn.1000-5641.2019.04.005 |
[1] |
KORSUNSKY S V. Soliton solutions for a second-order KdV equation[J]. Phys Lett A, 1994, 185:174-176. doi: 10.1016/0375-9601(94)90842-7
|
[2] |
LEE C T, LIU J L, LEE C C, et al. The second-order KdV equation and its soliton-like solution[J]. Modern Physics Letters B, 2009, 23:1771-1780. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f02152ebd057d13308d93224ec0e9d25
|
[3] |
LEE C C, LEE C T, LIU J L, et al. Quasi-solitons of the two-mode Korteweg-de Vries equation[J]. Eur Phys J Appl Phys, 2010, 52:11301. doi: 10.1051/epjap/2010132
|
[4] |
LEE C T. Some notes on a two-mode Korteweg-de Vries equation[J]. Phys Scr, 2010, 81:065006. doi: 10.1088/0031-8949/81/06/065006
|
[5] |
LEE C T, LIU J L. A Hamiltonian model and soliton phenomenon for a two-mode KdV equation[J]. Rocky Mt J Math, 2011, 41:1273-1289. doi: 10.1216/RMJ-2011-41-4-1273
|
[6] |
LEE C T, LEE C C. On wave solutions of a weakly nonlinear and weakly dispersive two-mode wave system[J]. Waves in Random and Complex Media, 2013, 23:56-76. doi: 10.1080/17455030.2013.770585
|
[7] |
LEE C T, LEE C C. Analysis of solitonic phenomenon for a two-mode KdV equation[J]. Physics of Wave Phenomena, 2014, 22:69-80. doi: 10.3103/S1541308X14010130
|
[8] |
LEE C T, LEE C C. On the study of a nonlinear higher order dispersive wave equation:Its mathematical physical structure and anomaly soliton phenomena[J]. Waves in Random and Complex Media, 2015, 25:197-222. doi: 10.1080/17455030.2014.1002441
|
[9] |
LEE C T, LEE C C. Symbolic computation on a second-order KdV equation[J]. Journal of Symbolic Computation, 2016, 74:70-95. doi: 10.1016/j.jsc.2015.06.006
|
[10] |
WAZWAZ A M. Multiple soliton solutions and other exact solutions for a two-mode KdV equation[J]. Math Methods Appl Sci, 2017, 40:2277-2283. http://d.old.wanfangdata.com.cn/Periodical/ccsxyyysx201802002
|
[11] |
LEE C T, LEE C C, LIU M L. Double-soliton and conservation law structures for a higher-order type of Korteweg-de Vries equation[J]. Physics Essays, 2015, 28:633-638. doi: 10.4006/0836-1398-28.4.633
|
[12] |
ALQURAN M, JARRAH A. Jacobi elliptic function solutions for a two-mode KdV equation[J/OL]. Journal of King Saud University-Science, (2017-07-03)[2018-06-28]. http://dx.doi.org/10.1016/j.jksus.2017.06.010.
|
[13] |
XIAO Z J, TIAN B, ZHEN H L, et al. Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid[J]. Waves in Random and Complex Media, 2017, 27:1-14. doi: 10.1080/17455030.2016.1185193
|
[14] |
WAZWAZ A M. A two-mode modified KdV equation with multiple soliton solutions[J]. Appl Math Lett, 2017, 70:1-6. doi: 10.1016/j.aml.2017.02.015
|
[15] |
WAZWAZ A M. A two-mode Burgers equation of weak shock waves in a fluid:Multiple kink solutions and other exact solutions[J]. Int J Appl Comput Math, 2017, 3:3977-3985. doi: 10.1007/s40819-016-0302-4
|
[16] |
WAZWAZ A M. A study on a two-wave mode Kadomtsev-Petviashvili equation:Conditions for multiple soliton solutions to exist[J]. Math Methods Appl Sci, 2017, 40:4128-4133. doi: 10.1002/mma.v40.11
|
[17] |
JARADAT H M, SYAM M, ALQURAN M. A two-mode coupled Korteweg-de Vries:Multiple-soliton solutions and other exact solutions[J]. Nonlinear Dyn, 2017, 90:371-377. doi: 10.1007/s11071-017-3668-x
|
[18] |
WAZWAZ A M. Two-mode fifth-order KdV equations:Necessary conditions for multiple-soliton solutions to exist[J]. Nonlinear Dyn, 2017, 87:1685-1691. doi: 10.1007/s11071-016-3144-z
|
[19] |
WAZWAZ A M. Two-mode Sharma-Tasso-Olver equation and two-mode fourth-order Burgers equation:Multiple kink solutions[J]. Alexandria Eng J, 2018, 57:1971-1976. doi: 10.1016/j.aej.2017.04.003
|
[20] |
JARDAT H M. Two-mode coupled Burgers equation:Multiple-kink solutions and other exact solutions[J]. Alexandria Eng J, 2018, 57:2151-2155. doi: 10.1016/j.aej.2017.06.014
|
[21] |
SYAM M, JARADAT H M, ALQURAN M. A study on the two-mode coupled modified Korteweg-de Vries using the simplified bilinear and the trigonometric-function methods[J]. Nonlinear Dyn, 2017, 90:1363-1371. doi: 10.1007/s11071-017-3732-6
|
[22] |
WAZWAZ A M. Two wave mode higher-order modified KdV equations:Essential conditions for multiple soliton solutions to exist[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2017, 27:2223-2230. doi: 10.1108/HFF-10-2016-0413
|
[23] |
HEREMAN W, NUSEIR A. Symbolic methods to construct exact solutions of nonlinear partial differential equations[J]. Mathematics and Computers in Simulation, 1997, 43:13-27. doi: 10.1016/S0378-4754(96)00053-5
|
[24] |
WAZWAZ A M. Single and multiple-soliton solutions for the (2+1)-dimensional KdV equation[J]. Appl Math Comput, 2008, 204:20-26. http://cn.bing.com/academic/profile?id=f151900e18b1a9ba049be9cb42c45d79&encoded=0&v=paper_preview&mkt=zh-cn
|
[25] |
ZUO J M, ZHANG Y M. The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq-Burgers equation[J]. Chin Phy B, 2011, 20:010205. doi: 10.1088/1674-1056/20/1/010205
|
[26] |
WAZWAZ A M. Multiple soliton solutions for the integrable couplings of the KdV and the KP equations[J]. Open Physics, 2013, 11:291-295. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.2478/s11534-013-0183-7
|
[27] |
WAZWAZ A M. Multiple kink solutions for two coupled integrable (2+1)-dimensional systems[J]. Appl Math Lett, 2016, 58:1-6. doi: 10.1016/j.aml.2016.01.019
|
[28] |
YU F J. Prolongation structure for nonlinear integrable couplings of a KdV soliton hierarchy[J]. Chin Phys B, 2012, 21:010201. doi: 10.1088/1674-1056/21/1/010201
|
[29] |
MALFLIET W, HEREMAN W. The tanh method:I. Exact solutions of nonlinear evolution and wave equations[J]. Phys Scr, 1996, 54:563-568. doi: 10.1088/0031-8949/54/6/003
|
[30] |
FAN E, HONA Y C. Generalized tanh method extended to special types of nonlinear equations[J]. Zeitschrift für Naturforschung A, 2002, 57:692-700. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zna-2002-0809
|
[31] |
WAZWAZ A M. The tanh method for traveling wave solutions of nonlinear equations[J]. Appl Math and Comput, 2004, 154:713-723. http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_bf5e77d9ce9f44d9b18fe7f89b90cf5f
|
[32] |
LIU S, FU Z, LIU S, et al. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations[J]. Phys Lett A, 2001, 289:69-74. doi: 10.1016/S0375-9601(01)00580-1
|