具任意次非线性项的Camassa-Holm方程的双孤子新解

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

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.

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 l, with 2 auxiliary equations, the function transformation and the variable separation solutions, the problem of solving the arbi- trary 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 conclu- sions on the auxiliary equation, the new 2-soliton and 2-period solutions were constructed.