Conservative finite difference schemes for the generalized Zakharov-Kuznetsov equations

被引：8

作者：

Nishiyama, Hirota ^{[1
]}

Noi, Takahiro ^{[1
]}

Oharu, Shinnosuke ^{[1
]}

机构：

[1] Chuo Univ, Dept Math, Tokyo 112, Japan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2012年 / 236卷 / 12期

关键词：

Generalized Zakharov-Kuznetsov equation; Discrete variational method; Conservative finite difference scheme; Division and collision of nonlinear waves; SHALLOW-WATER EQUATIONS; WAVES; SOLITONS;

D O I：

10.1016/j.cam.2011.04.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the construction of conservative finite difference schemes by means of discrete variational method for the generalized Zakharov-Kuznetsov equations and the numerical solvability of the two-dimensional nonlinear wave equations. A finite difference scheme is proposed such that mass and energy conservation laws associated with the generalized Zakharov-Kuznetsov equations hold. Our arguments are based on the procedure that D. Furihata has recently developed for real-valued nonlinear partial differential equations. Numerical results are given to confirm the accuracy as well as validity of the numerical solutions and then exhibit remarkable nonlinear phenomena of the interaction and behavior of pulse wave solutions. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2998 / 3006

页数：9

共 17 条

[1] On the energetic Galerkin boundary element method applied to interior wave propagation problems [J].