Finding the One-Loop Soliton Solution of the Short-Pulse Equation by Means of the Homotopy Analysis Method

被引：6

作者：

Parkes, E. J. ^{[2
]}

Abbasbandy, S. ^{[1
]}

机构：

[1] Imam Khomeini Int Univ, Dept Math, Ghazvin 3414916819, Iran

[2] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark, Scotland

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 25卷 / 02期

关键词：

short-pulse equation; homotopy analysis method; solitary-wave solution; series solution; BOUNDARY-LAYER-FLOWS; ANALYTIC SOLUTION; NONLINEAR EQUATIONS; SERIES SOLUTIONS; 2ND-GRADE FLUID; HEAT-TRANSFER; KDV EQUATION; WAVES; PLATE; SHEET;

D O I：

10.1002/num.20348

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 401-408, 2009

引用

页码：401 / 408

页数：8

共 31 条

[1] Homotopy analysis method for generalized Benjamin-Bona-Mahony equation [J].

Abbasbandy, S. .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2008, 59 (01) :51-62

[2] Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method [J].

Abbasbandy, S. ;

Parkes, E. J. .

CHAOS SOLITONS & FRACTALS, 2008, 36 (03) :581-591

[3] Soliton solutions for the fifth-order KdV equation with the homotopy analysis method [J].

Abbasbandy, S. ;

Zakaria, F. Samadian .

NONLINEAR DYNAMICS, 2008, 51 (1-2) :83-87

[4] Newton-homotopy analysis method for nonlinear equations [J].

Abbasbandy, S. ;

Tan, Y. ;

Liao, S. J. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (02) :1794-1800

[5] Homotopy analysis method for heat radiation equations [J].

Abbasbandy, S. .

INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, 2007, 34 (03) :380-387

[6] The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation [J].

Abbasbandy, S. .

PHYSICS LETTERS A, 2007, 361 (06) :478-483

[7] The application of homotopy analysis method to nonlinear equations arising in heat transfer [J].

Abbasbandy, S. .

PHYSICS LETTERS A, 2006, 360 (01) :109-113

[8]

ABBASBANDY S, APPL MATH M IN PRESS

[9] A note on series solution for generalized Couette flow [J].

Hayat, T. ;

Sajid, M. ;

Ayub, M. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2007, 12 (08) :1481-1487

[10] On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet [J].

Hayat, T. ;

Abbas, Z. ;

Sajid, M. .

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2007, 74 (06) :1165-1171

← 1 2 3 4 →