广义Korteweg-de Vries方程的数值行波解(英文)

Numerical Traveling Wave Solution for the General Korteweg-de Vries Equation

导出

摘要本文构造了求解广义Korteweg-de Vries(KdV)方程的新的指数型有限差分格式.利用该格式获得了一些近似行波解.数值解与精确解的比较显示了该格式的效率. A new exponential finite difference method is constructed and used for solving the general Korteweg - de Vries （KdV） equation. Some approximate traveling wave solutions are obtained. Comparisons between numerical traveling wave solutions and the exact solutions reveal the efficiency of the scheme.

作者赵国忠

机构地区包头师范学院数学科学学院

出处《阴山学刊（自然科学版）》 2014年第4期5-10,共6页 Yinshan Academic Journal(Natural Science Edition)

基金国家自然科学基金(11261035) 内蒙古高等学校科学研究基金重点项目(NJZZ12198) 内蒙古自然科学基金(2012MS0102)资助项目

关键词广义KDV方程指数型有限差分格式行波解 General KdV equation Exponential finite difference method Traveling wave solution

分类号 O241.82 [理学—计算数学]

引文网络
相关文献

参考文献13

1Helal M A, Mehanna M S. A comparative study between two different methods for solving the general Korteweg -de Vries equation (GKdV) [ J ]. Chaos, Solitons & Fractals, 2007, 33 : 725 - 739.
2Feng Z S, Knobel R. Traveling waves to a Burgers - Korte- weg - de Vries - type equation with higher - order nonlinear- ities [J]. J. Math. Anal. Appl., 2007, 328: 1435- 1450.
3Zhang W G, Chang Q S, Jiang BG. Explicit exact solitary -wave solutions for compound KdV -type and compound KdV - Burgers - type equations with nonlinear term of any order [J]. Chaos, Solitons & Fractals, 2002, 13:311 - 319.
4Feng Z. Traveling solitary wave solutions to evolution equa- tions with nonlinear terms of any order [ J ]. Chaos, Solitons & Fractals, 2003, 17:861 -868.
5Li B, Chen Y, Qing Z H. Explicit exact solutions for new general two - dimensional KdV - type and two - dimension- alKdV - Burgers - type equations with nonlinear term of any order [J].J. Phys. A, 2002, 35:8253-8265.
6Parkes E J, Duffy B R. An automated tanh -fucntion meth- od for finding solitat7 wave solutions to nonlinear evolution equations [J]. Comput. Phys. Comm., 1996, 98: 288- 300.
7Parkes E J, Duffy B R. Traveling solitary wave solutions to a compound KdV- Burgers equation [ J] Phys. Lett. A, 1997, 229:217-220.
8Wang M L. Exact solutions for a compound KdV - Burgers equation [J]. Phys. Lett. A, 1996, 213: 279-287.
9Feng Z. On explicit exact solutions to the compound Burgers - Korteweg - de Vries equation [ J ]. Phys. Left. A, 2002, 293 : 57 - 66.
10Khater A H, E1Kalaawy O H, Helal M A. Two new clas- ses of exact solutions for the KdV equation via Backlund transformations [ J ]. Chaos, Solitons & Fractals, 1997, 8 : 1901 - 1909.

1田强,赵国忠.Burgers方程的指数型差分格式[J].内蒙古大学学报（自然科学版）,2009,40(1):37-41. 被引量：3
2王治安,蒋咪娜.广义Korteweg-de Vries-Burgers方程解的一致估计(英文)[J].华中师范大学学报（自然科学版）,2001,35(3):264-266.
3曹庆杰,于行洲.一类广义KdV方程多孤立子相互作用的差分方法[J].辽宁师范大学学报（自然科学版）,1997,20(1):1-8. 被引量：3
4张领海.从等离子体物理中提出的广义Korteweg-de Vries方程解的L^2一致稳定性(英文)[J].数学进展,1997,26(6):537-544.
5张天德,鲁统超,左进明,曹庆杰.高阶广义KDV方程和KP方程的数值解法[J].系统科学与数学,2005,25(6):658-668. 被引量：6
6刘广军,段广森.非线性弹性杆内纵向波方程的孤立波解[J].河南师范大学学报（自然科学版）,2001,29(3):101-103. 被引量：3

阴山学刊（自然科学版）

2014年第4期

浏览历史

内容加载中请稍等...

广义Korteweg-de Vries方程的数值行波解(英文)

参考文献13

相关作者

相关机构

相关主题

浏览历史