EXACT SOLITON SOLUTIONS OF THE VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNTIONS

YAN ZHEN-YA; ZHANG HONG-QING

doi:10.7498/aps.48.1957

Abstract
In this paper,first,by using a new transformation,the variable coefficient KdV-MKdV equation is reduced to a third-order nonlinear ordinary differential equation (NODE),and then several exact soliton-solutions for the variable coefficient KdV-MKdV equatioin are obtained through considering this NODE.The method can be also used to solve other nonlinear equations,such as the variable coefficient KP equation,sine-Gordon equation and so on.
Authors and contacts
YAN ZHEN-YA,

ZHANG HONG-QING

1.
大连理工大学数学科学研究所，大连 116024
References

Cited By

[1]	Liu Yong, Liu Xi-Qiang. Exact solutions of Whitham-Broer-Kaup equations with variable coefficients. Acta Physica Sinica, 2014, 63(20): 200203. doi: 10.7498/aps.63.200203
[2]	Ding Qi, Hao Ai-Jing. Differential invariants for CDG equation and coupled KDV-MKDV equations. Acta Physica Sinica, 2014, 63(11): 110503. doi: 10.7498/aps.63.110503
[3]	Yi Li-Na, Taogetusang. New complex soliton-like solutions of combined KdV equation with variable coefficients and forced term. Acta Physica Sinica, 2014, 63(3): 030201. doi: 10.7498/aps.63.030201
[4]	Wan Hui. Exact solutions to the nonlinear diffusion-convection equation with variable coefficients and source term. Acta Physica Sinica, 2013, 62(9): 090203. doi: 10.7498/aps.62.090203
[5]	Zhao Xing-Tao, Zheng Yi, Liu Xiao-Xu, Liu Zhao-Lun, Li Shu-Guang, Hou Lan-Tian. Simulation of photonic crystal fiber with three and four zero-dispersion wavelengths. Acta Physica Sinica, 2012, 61(19): 194210. doi: 10.7498/aps.61.194210
[6]	Taogetusang, Bai Yu-Mei. New type infinite sequence exact solutions of the second KdV equation with variable coefficients. Acta Physica Sinica, 2012, 61(6): 060201. doi: 10.7498/aps.61.060201
[7]	Taogetusang, Sirendaoerji. A method for constructing exact solutions of nonlinear evolution equation with variable coefficients. Acta Physica Sinica, 2009, 58(4): 2121-2126. doi: 10.7498/aps.58.2121
[8]	Wu Hai-Yan, Zhang Liang, Tan Yan-Ke, Zhou Xiao-Tao. Some new exact Jacobian elliptic function solutions of three kinds of nonlinear evolution equations. Acta Physica Sinica, 2008, 57(6): 3312-3318. doi: 10.7498/aps.57.3312
[9]	Taogetusang, Sirendaoerji. The auxiliary equation for constructing the exact solutions of the variable coefficient combined KdV equation with forcible term. Acta Physica Sinica, 2008, 57(3): 1295-1300. doi: 10.7498/aps.57.1295
[10]	Mao Jie-Jian, Yang Jian-Rong. New solitary-wave-like solutions and exact solutions to variable coefficient generalized KdV equation. Acta Physica Sinica, 2007, 56(9): 5049-5053. doi: 10.7498/aps.56.5049
[11]	Pan Jun-Ting, Gong Lun-Xun. Jacobi elliptic function solutions to the coupled KdV-mKdV equation. Acta Physica Sinica, 2007, 56(10): 5585-5590. doi: 10.7498/aps.56.5585
[12]	Lu Dian-Chen, Hong Bao-Jian, Tian Li-Xin. Explicit and exact solutions to the variable coefficient combined KdV equation with forced term. Acta Physica Sinica, 2006, 55(11): 5617-5622. doi: 10.7498/aps.55.5617
[13]	Mao Jie-Jian, Yang Jian-Rong. New solitary wave-like solution and exact solution of variable coefficient KP equation. Acta Physica Sinica, 2005, 54(11): 4999-5002. doi: 10.7498/aps.54.4999
[14]	Wei Cai-Min, Xia Zun-Quan, Tian Nai-Shuo. New exact soliton-like solution for a generalized stochastic KdV equation. Acta Physica Sinica, 2005, 54(6): 2463-2467. doi: 10.7498/aps.54.2463
[15]	Shi Yu-ren, Lü Ke-Pu, Duan Wen-Shan, Hong Xue-Ren, Zhao Jin-Bao, Yang Hong-Juan. Explicit and exact solutions of the combined KdV equation. Acta Physica Sinica, 2003, 52(2): 267-270. doi: 10.7498/aps.52.267
[16]	Li De-Sheng, Zhang Hong-Qing. Improved tanh-function method and the new exact solutions for the general variab le coefficient KdV equation and MKdV equation. Acta Physica Sinica, 2003, 52(7): 1569-1573. doi: 10.7498/aps.52.1569
[17]	ZHANG JIE-FANG, CHEN FANG-YUE. TRUNCATED EXPANSION METHOD AND NEW EXACT SOLITON-LIKE SOLUTION OF THE GENERAL VARIABLE COEFFICIENT KdV EQUATION. Acta Physica Sinica, 2001, 50(9): 1648-1650. doi: 10.7498/aps.50.1648
[18]	Ruan Hang-Yu, Chen Yi-Xin. . Acta Physica Sinica, 2000, 49(2): 177-180. doi: 10.7498/aps.49.177
[19]	ZHU ZUO-NONG. SOLITON-LIKE SOLUTIONS OF GENERALIZED KdV EQUA-TION WITH EXTERNAL FORCE TERM. Acta Physica Sinica, 1992, 41(10): 1561-1566. doi: 10.7498/aps.41.1561
[20]	LOU SEN-YUE, RUAN HANG-YU. CONSERVATION LAWS OF THE VARIABLE COEFFICIENT KdV AND MKdV EQUATIONS. Acta Physica Sinica, 1992, 41(2): 182-187. doi: 10.7498/aps.41.182

Catalog

Vol. 48, Issue 11 - 1999-06-05

Metrics

Abstract views: 7435
PDF Downloads: 882
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

EXACT SOLITON SOLUTIONS OF THE VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNTIONS

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

EXACT SOLITON SOLUTIONS OF THE VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNTIONS

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About