具任意次非线性项的Camassa-Holm方程的双孤子新解

套格图桑

doi:10.21656/1000-0887.370211

具任意次非线性项的Camassa-Holm方程的双孤子新解

doi: 10.21656/1000-0887.370211

套格图桑

内蒙古师范大学数学科学学院, 呼和浩特 010022

基金项目: 国家自然科学基金(11361040)；内蒙古自治区自然科学基金(2015MS0128)；内蒙古自治区高等学校科学研究基金(NJZY16180)

详细信息

作者简介:
套格图桑（1963—），男，教授，博士(E-mail: tgts@imnu.edu.cn).

中图分类号: O175
计量
- 文章访问数: 1161
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- 被引次数: 0
出版历程
- 收稿日期: 2016-07-01
- 修回日期: 2016-08-24
- 刊出日期: 2017-05-15

New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation

Taogetusang

Mathematics Science College, Inner Mongolia Normal University, Huhhot 010022, P.R.China

Funds: The National Natural Science Foundation of China(11361040)

摘要

摘要: 给出辅助方程、函数变换与变量分离解相结合的方法,构造了具任意次非线性项的Camassa-Holm方程的双孤子和双周期新解.首先，通过两个辅助方程、函数变换与变量分离解,将具任意次非线性项的Camassa-Holm方程的求解问题转化为非线性代数方程的求解问题.然后，借助符号计算系统Mathematica求出该方程组的解,并用辅助方程的相关结论,构造了双周期解和双孤子新解.
- 函数变换 /
- 变量分离解 /
- 具任意次非线性项的Camassa-Holm方程 /
- 双孤子新解
Abstract: The method combining the auxiliary equation, the function transformation and the variable separation solutions was proposed to construct the new 2-soliton and 2-period solutions to the arbitrary order nonlinear Camassa-Holm equation. Step 1, with 2 auxiliary equations, the function transformation and the variable separation solutions, the problem of solving the arbitrary order nonlinear Camassa-Holm equation was transformed to the problem of solving the nonlinear algebraic equations. Step 2, by means of symbolic computation system Mathematica, the solutions to the algebraic equations were obtained, and with the help of the relative conclusions on the auxiliary equation, the new 2-soliton and 2-period solutions were constructed.
- function transformation /
- variable separation solution /
- arbitrary order nonlinear Camassa-Holm equation /
- new 2-soliton solution

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参考文献(10)

[1]	Camassa R, Holm D D. An integrable shallow water equation with peaked solitons[J]. Phys Rev Lett,1993,71(13): 1661-1664.
[2]	殷久利, 田立新. 一类非线性方程的compacton解及其移动compacton 解[J]. 物理学报, 2004,53(9): 2821-2827.(YIN Jiu-li, TIAN Li-xin. Compacton solutions and floating compacton solutions of one type of nonlinear equations[J]. Acta Physica Sinica,2004,53(9): 2821-2827.(in Chinese))
[3]	CHEN Yong, LI Biao. New exact travelling wave solutions for generalized Zakharov-Kuznetsov equations using general projective Riccati equation method[J]. Commun Theor Phys,2004,41(1): 1-6.
[4]	Sirendaoerji, SUN Jong. Adirect method for solving sine-Gordon type equations[J]. Phys Lett A ,2002,298(3):133-139.
[5]	Gepreel K A, Omran S. Exact solutions for nonlinear partial fractional differential equations[J]. Chinese Physics B,2012,21(11): 110204.
[6]	Alam M N, Akbar M A, Mohyud-Din S T. A novel (G′/G) -expansion method and its application to the Boussinesq equation[J]. Chinese Physics B,2014,23(2): 020203.
[7]	马松华, 方建平. 扩展的(2+1)维浅水波方程的尖峰孤子解及其相互作用[J]. 物理学报, 2012,61(18): 180505-1-180505-6.(MA Song-hua, FANG Jian-ping. Peaked soliton solutions and interaction between solitons for the extended (2+1)-dimensional shallow water wave equation[J]. Acta Physica Sinica,2012,61(18): 180505-1-180505-6.(in Chinese))
[8]	套格图桑, 白玉梅. 非线性发展方程的Riemann theta 函数等几种新解[J]. 物理学报, 2013,62(10): 100201-1-100201-9.(Taogetusang, BAI Yu-mei. Riemann theta function and other several kinds of new solutions of nonlinear evolution equations[J]. Acta Physica Sinica,2013,62(10): 100201-1-100201-9.(in Chinese))
[9]	杨小锋, 邓子辰, 魏乙. 基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解[J]. 应用数学和力学, 2015,36(10): 1067-1075.(YANG Xiao-feng, DENG Zi-chen, WEI Yi. Traveling wave solutions to the Davey-Stewartson equation with the Riccati-Bernoulli sub-ODE method[J]. Applied Mathematics and Mechanics,2015,36(10): 1067-1075.(in Chinese))
[10]	那仁满都拉, 额尔敦仓. 立方非线性微结构固体中的对称孤立波及存在条件[J]. 应用数学和力学,2014,35(11):1210-1217.(Narenmandula, Eerduncang. Symmetric solitary waves and their existence conditions in cubic nonlinear microstructured solids[J]. Applied Mathematics and Mechanics,2014,35(11): 1210-1217.(in Chinese))