The new exact solutions of Volterra difference-differential equation and KdV difference-differential equation

Taogetusang; Sirendaoerji

doi:10.7498/aps.58.5887

Abstract
Based on the auxiliary equation method and the trial function method, a method for combining function transformation with auxiliary equation is proposed. And the method is applied to construct new exact solitary wave solutions and triangle function solutions of Volterra and KdV difference-differential equations with the help of symbolic computation system Mathematica. Our method can also be applied to other nonlinear difference-differential equations.

Keywords:
auxiliary equation /

function transformation /

nonlinear difference-differential equation /

solitary wave solution
Authors and contacts
Taogetusang²,

Sirendaoerji¹

(1); (2)内蒙古师范大学数学科学学院,呼和浩特 010022
References

Cited By

[1]	Taogetusang, Yi Li-Na. New complexion two-soliton solutions of a class of nonlinear evolution equation. Acta Physica Sinica, 2015, 64(2): 020201. doi: 10.7498/aps.64.020201
[2]	Taogetusang, Yi Li-Na. New infinite sequence solutions to equations of sine-Gordon type. Acta Physica Sinica, 2014, 63(21): 210202. doi: 10.7498/aps.63.210202
[3]	Taogetusang, Yi Li-Na. New infinite sequence soliton-like solutions of Camassa-Holm-r equation. Acta Physica Sinica, 2014, 63(12): 120201. doi: 10.7498/aps.63.120201
[4]	Xu Yuan-Fen. Exact traveling wave solutions for simplified model of Gross-Pitaevskii equation in the 1D-Tonks-Girardeau gas. Acta Physica Sinica, 2013, 62(10): 100202. doi: 10.7498/aps.62.100202
[5]	Taogetusang, Bai Yu-Mei. A method of constructing infinite sequence soliton-like solutions of nonlinear evolution equations. Acta Physica Sinica, 2012, 61(13): 130202. doi: 10.7498/aps.61.130202
[6]	Taogetusang. New infinite sequences exact solutions to sine-Gordon-type equations. Acta Physica Sinica, 2011, 60(7): 070203. doi: 10.7498/aps.60.070203
[7]	Yang Pei, Chen Yong, Li Zhi-Bin. Analytic approximation for the soliton solution of the discrete modified KdV equation. Acta Physica Sinica, 2010, 59(6): 3668-3673. doi: 10.7498/aps.59.3668
[8]	Taogetusang. New infinite sequence exact solutions to the general lattice. Acta Physica Sinica, 2010, 59(10): 6712-6718. doi: 10.7498/aps.59.6712
[9]	Gao Bin, Liu Shi-Da, Liu Shi-Kuo. Envelope periodic and solitary solutions of Davey-Stewartson equation. Acta Physica Sinica, 2009, 58(4): 2155-2158. doi: 10.7498/aps.58.2155
[10]	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
[11]	Taogetusang, Sirendaoerji. Constructing new exact solutions to nonlinear difference-differential equations by Riccati equation. Acta Physica Sinica, 2009, 58(9): 5894-5902. doi: 10.7498/aps.58.5894
[12]	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
[13]	. Solving solitary wave solutions of higher dimensional nonlinear evolution equations with the homotopy analysis method. Acta Physica Sinica, 2007, 56(12): 6791-6796. doi: 10.7498/aps.56.6791
[14]	Yang Hong-Juan, Shi Yu-Ren, Duan Wen-Shan, Lü Ke-Pu. Solving solitary wave solutions of nonlinear evolution equations with the homotopy analysis method. Acta Physica Sinica, 2007, 56(6): 3064-3069. doi: 10.7498/aps.56.3064
[15]	Taogetusang, Sirendaoerji. Constructing the exact solutions of the (2+1)-dimensional Hybrid-Lattice and discrete mKdV equation. Acta Physica Sinica, 2007, 56(2): 627-636. doi: 10.7498/aps.56.627
[16]	Taogetusang, Sirendaoerji. New exact solitary wave solutions for nonlinear wave equation with fifth-order strong nonlinear term constructed by hyperbolic function type of auxiliary equation. Acta Physica Sinica, 2006, 55(1): 13-18. doi: 10.7498/aps.55.13
[17]	Huang Ding-Jiang, Zhang Hong-Qing. Extended hyperbolic function method and new exact solitary wave solutions of Zakharov equations. Acta Physica Sinica, 2004, 53(8): 2434-2438. doi: 10.7498/aps.53.2434
[18]	Taogetusang, Sirendaoreji. New exact solitary wave solutions to the BBM and mBBM equations. Acta Physica Sinica, 2004, 53(12): 4052-4060. doi: 10.7498/aps.53.4052
[19]	Zhang Shan-Qing, Li Zhi-Bin. A new application of Jacobi elliptic function expansion method. Acta Physica Sinica, 2003, 52(5): 1066-1070. doi: 10.7498/aps.52.1066
[20]	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

Catalog

Vol. 58, Issue 9 - 2009-05-05

Metrics

Abstract views: 8914
PDF Downloads: 1381
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

The new exact solutions of Volterra difference-differential equation and KdV difference-differential equation

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

The new exact solutions of Volterra difference-differential equation and KdV difference-differential equation

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About