三类势能mKdV方程解的物理结构

Physical Structures for Three Kinds of Potential mKdV Equations

在降阶法的基础上,本文采用一种求解微分方程的数学方法,研究了两个(1+1)维势能mKdV方程和一个(2+1)维势能mKdV方程,得到了这三个方程行波解的解析表达式。对于(1+1)维具有正或负指数的mKdV方程,我们指出了波函数u的指数连同波速与方程中最高阶微分项的系数的比值一起决定着解的物理结构。

A mathematical technique based on the reduction of order for solving differential equations is developed to investigate two types of potential mKdV equations in （1 ＋ 1） dimensions and a potential rnKdV equation in （2 ＋ 1） dimensions. The analytical expressions of travelling wave solutions for the three equations are derived. For the （1 ＋ 1） dimensional mKdV equation with positive or negative exponents, it is shown that the exponent of wave function u and the ratio between the wave speed and the variant coefficient of the highest differential term in the equation determine the physical structures of the solutions.