一类非线性发展方程的复合型双孤子新解∗

摘要

通过下列步骤，构造了一类非线性发展方程的无穷序列复合型双孤子新解：步骤一，给出两种函数变换，把一类非线性发展方程化为二阶非线性常微分方程；步骤二，再通过函数变换，二阶非线性常微分方程转化为一阶非线性常微分方程组，并获得了该方程组的首次积分；步骤三，利用首次积分与两种椭圆方程的新解与Bäcklund变换，构造了一类非线性发展方程的无穷序列复合型双孤子新解。%New infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation are constructed with the help of function transformations and two kinds of elliptic equations. Step one,according to two function transformations, a kind of nonlinear evolution equation is changed into a nonlinear ordinary differential equation of second order. Step two, using function transformation, the nonlinear ordinary differential equation of second order is transformed into a set of nonlinear ordinary differential equations of first order, and the first integral of the set of equations is obtained. Finally, the first integral with new solutions and Bäcklund transformation of two kinds of elliptic equations are used to search for new infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation.