新的辅助方程法构造KdV方程的行波解

庞晶; 边春泉; 朝鲁

doi:10.3879/j.issn.1000-0887.2010.07.014

新的辅助方程法构造KdV方程的行波解

doi: 10.3879/j.issn.1000-0887.2010.07.014

1.
内蒙古工业大学理学院, 呼和浩特 010051;2.上海海事大学数学系, 上海 200315

基金项目: 国家自然科学基金资助项目(10461005);国家教育部博士点基金资助项目(20070128001);内蒙古高等教育资助课题(NJZY08057)

详细信息

作者简介:
庞晶(1963- ),男,山西大同人,教授(联系人.Tel:+86-471-6576181;E-mail:pang_@jmiut.edu.cn;bianchunquan2005@163.com).

中图分类号: O175.29;O241.82
计量
- 文章访问数: 1684
- HTML全文浏览量: 148
- PDF下载量: 1048
- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-05-05
- 刊出日期: 2010-07-15

New Auxiliary Equation Method for Solving the KdV Equation

1.
College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China;

摘要

摘要: 应用一种新的辅助方程法成功地获得了(1+1)维KdV方程的多个含有参数的精确行波解,所得的解涵盖了已有结果．与其它方法相比,所给出的方法具有简单高效、计算量小、速度快、易于求解等特点．另外,所给的方法还可以用来求解其它的一大类非线性发展方程的精确行波解．
- 辅助方程法 /
- 行波法 /
- KdV方程 /
- 齐次平衡法
Abstract: A new auxiliary equation method was used to find exact travelling wave solutions to the (1+1)-dmiensional KdV equation. Some exact travelling wave solutions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.
- auxiliary equation method /
- travelling wave solution /
- KdV equation /
- homogeneous balance method

HTML全文

参考文献(21)

[1]	李志斌. 非线性数学物理方程的行波解[M]. 北京: 科学出版社, 2006.
[2]	刘式适, 刘式达. 物理学中的非线性方程[M]. 北京: 北京大学出版社, 2000.
[3]	楼森岳, 唐晓艳. 非线性数学物理方法[M]. 北京: 科学出版社, 2006.
[4]	李翊神. 孤子与可积系统[M]. 上海: 上海科技教育出版社, 1999.
[5]	M·B·A·曼索. 非线性耗散-色散方程行波解的存在性[J]. 应用数学和力学, 2009, 30(4): 479- 483.
[6]	Wazwaz A M. The tanh method for travelling wave solutions of nonlinear equations[J]. Appl Math Comput, 2004, 154(3):713-723. doi: 10.1016/S0096-3003(03)00745-8
[7]	邓镇国, 马和平. 广义 KdV 方程Fourier谱逼近的最优误差估计 [J]. 应用数学和力学, 2009 , 30(1) :30-39.
[8]	套格图桑, 斯仁道尔吉. 新的辅助方程法构造非线性发展方程的孤立波解[J]. 内蒙古大学学报(自然科学版), 2004, 35(3):0246-0251.
[9]	ZHANG Sheng, XIA Tie-cheng. A generalized new auxiliary equation method and its applications to nonlinear partial differential equations[J]. Phys Lett A, 2007, 363(5/6):356-360. doi: 10.1016/j.physleta.2006.11.035
[10]	李保安, 尤国伟, 秦青. BBM方程的周期波解和孤立波解[J]. 河南科技大学学报(自然科学版), 2004, 25(5):70-73.
[11]	Wazwaz A M. A sine-cosine method for handling nonlinear wave equations[J]. Math Comput Modelling, 2004, 40(5/6): 499-508. doi: 10.1016/j.mcm.2003.12.010
[12]	ZHANG Sheng. Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations[J]. Computers Mathematics with Applications, 2008, 56(5): 1451-1456. doi: 10.1016/j.camwa.2008.02.045
[13]	WANG Ming-liang, LI Xiang-zheng, ZHANG Jing-liang. The (G/G′)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics[J]. Phys Lett A, 2008 , 372(4):417- 423.
[14]	Bekir A. Application of the (G/G′)-expansion method for nonlinear evolution equations[J]. Phys Lett A, 2008, 372(19): 3400-3406. doi: 10.1016/j.physleta.2008.01.057
[15]	ZHANG Jiao, WEI Xiao-li, LU Yong-jie. A generalized (G/G′)-expansion method and its applications[J]. Phys Lett A, 2008, 372(20): 3653-3658. doi: 10.1016/j.physleta.2008.02.027
[16]	ZHANG Sheng, TONG Jing-lin, WANG Wei. A generalized (G/G′)-expansion method for the mKdV equation with variable coefficients[J]. Phys Lett A, 2008, 372(13): 2254-2257. doi: 10.1016/j.physleta.2007.11.026
[17]	BIAN Chun-quan, PANG Jing, JIN Ling-hua, YING Xiao-mei. Solving two fifth order strong nonlinear evolution equations by using the (G/G′)-expansion method[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(9): 2337-2343. doi: 10.1016/j.cnsns.2009.10.006
[18]	Wazwaz A M. Compactons, solitons and periodic solutions for variants of the KdV and the KP equations[J]. Appl Math Comput, 2005, 161(2):561-575. doi: 10.1016/j.amc.2003.12.049
[19]	Schiesser W E. Method of lines solution of the Korteweg-de Vries equation[J]. Comput Math Appl, 1994, 28(10/12):147-154. doi: 10.1016/0898-1221(94)00190-1
[20]	Yomba E. The extended Fan’s sub-equation method and its application to KdV-mKdV, BKK and variant Boussinesq equations[J]. Phys Lett A, 2005 , 336(6):463-476.
[21]	Wazwaz A M. Distinct variants of the KdV equation with compact and noncompact structures[J]. Appl Math Comput, 2004, 150(2):365-377. doi: 10.1016/S0096-3003(03)00238-8