| 具任意次非线性项的Camassa-Holm方程的双孤子新解 |
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| 引用本文： | 套格图桑.具任意次非线性项的Camassa-Holm方程的双孤子新解[J].应用数学和力学,2017,38(5):553-560. |
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| 作者姓名： | 套格图桑 |
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| 作者单位： | 内蒙古师范大学 数学科学学院, 呼和浩特 010022 |
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| 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)The National Natural Science Foundation of China(11361040) |
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| 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.
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| 关 键 词： | 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 |
| 收稿时间： | 2016-07-01 |
New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation |
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| Institution: | Mathematics Science College, Inner Mongolia Normal University, Huhhot 010022, P.R.China |
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| 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. |
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| Keywords: | function transformation variable separation solution arbitrary order nonlinear Camassa-Holm equation new 2-soliton solution |
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