Exact solutions for the KdV-mKdV equation with time-dependent coefficients using the modified functional variable method

被引：4

作者：

Djoudi, W. ^{[1
]}

Zerarka, A. ^{[1
]}

机构：

[1] Univ Med Khider, Lab Appl Math, BP145, Biskra 07000, Algeria

来源：

COGENT MATHEMATICS | 2016年 / 3卷

关键词：

nonlinear soliton; travelling wave solutions; functional variable; homogeneous balance; KdV-mKdV;

D O I：

10.1080/23311835.2016.1218405

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, the functional variable method (fvm for short) is introduced to establish new exact travelling solutions of the combined KdV-mKdV equation. The technique of the homogeneous balance method is used in second stage to handle the appropriated solutions. We show that, the method is straightforward and concise for several kinds of nonlinear problems. Many new exact travelling wave solutions are successfully obtained.

引用

页数：8

共 26 条

[1] MODEL EQUATIONS FOR LONG WAVES IN NONLINEAR DISPERSIVE SYSTEMS [J].

BENJAMIN, TB ;

BONA, JL ;

MAHONY, JJ .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 272 (1220) :47-+

[2] An inverse scattering scheme for the regularized long-wave equation [J].

Dye, JM ;

Parker, A .

JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (05) :2889-2904

[3] Applications of the Jacobi elliptic function method to special-type nonlinear equations [J].

Fan, EG ;

Zhang, H .

PHYSICS LETTERS A, 2002, 305 (06) :383-392

[4] SHALLOW WATER WAVES ON SHEAR FLOWS [J].

FREEMAN, NC ;

JOHNSON, RS .

JOURNAL OF FLUID MECHANICS, 1970, 42 :401-&

[5] EXACT SOLUTION OF KORTEWEG-DE VRIES EQUATION FOR MULTIPLE COLLISIONS OF SOLITONS [J].

HIROTA, R .

PHYSICAL REVIEW LETTERS, 1971, 27 (18) :1192-+

[6] NEW NUMERICAL-SOLUTION OF THE KORTEWEG-DEVRIES EQUATION [J].

ISKANDAR, L .

APPLIED NUMERICAL MATHEMATICS, 1989, 5 (03) :215-221

[7]

Jinquing F., 1992, P INT WORKSH MATH ME, P1992

[8] Artificial perturbation for solving the Korteweg-de Vries equation [J].

Khelil N. ;

Bensalah N. ;

Saidi H. ;

Zerarka A. .

Journal of Zhejiang University-SCIENCE A, 2006, 7 (12) :2079-2082

[9]

Korteweg D J, 1895, PHILOS MAG, V5, P422, DOI DOI 10.1080/14786449508620739

[10] A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms [J].

Li, Xiangzheng ;

Wang, Mingliang .

PHYSICS LETTERS A, 2007, 361 (1-2) :115-118

← 1 2 3 →