非线性“loop”孤子方程的确定解

Exact solution of the nonlinear “loop” soliton equation

提出一种求解非线性“loop”孤子方程确定解的新方法,即以“行波”为因子,利用幂级数直接求解该方程解析函数U(ξ),用MatLab绘制c→光速和c→声速的U(ξ)_ξ图像,直接观察该方程解的变化规律,找出该方程的确定解(含孤波解).该方法为求解难度大的非线性孤子方程提供借鉴.

In this paper the author proposes a new method to solve the nonlinear “loop” soliton equation, that is, to directly find the solution of the analytic function U（ξ） of the equation by using the traveling wave parameter ξ and the power series expansion, and to find the exact solution of the equation （ including the solitary wave solution） by directly observing the variation of the equation using MatLab to depict the functional relationship of U（ξ）-ξ for the cases of c→light speed and c→sound speed. This method should be helpful in solving difficult nonlinear soliton equations.