非线性Schrdinger方程的包络形式解

Envelope solutions to nonlinear Schrdinger equation

扩展了最近提出的F展开方法以构造非线性演化方程更多的精确解,即将F展开法中的一阶非线性常微分方 程和单变量的有限幂级数代之以类似的一阶常微分方程组和两个变量的有限幂级数,这两个变量是一阶常微分方 程组的解分量.作为例子,用扩展的F展开法解非线性Schr dinger方程,得到了很丰富的包络形式的精确解,特别 是以两个不同的Jacobi椭圆函数表示的解.显然,扩展的F展开方法也可以解其他类型的非线性演化方程.

F-expansion method proposed recently is extended to construct more exact solutions of nonlinear evolution equations. To be more precise,it means that instead of the first-order ordinary differential equation(ODE) and finite power series of one variable in F-expansion method,we introduce similar first-order ODEs and finite power series of two variables,each one of which is the component of solution to ODEs. As an illustrative example,using this extended F-expansion method we solve nonlinear Schrdinger(NLS) equation,an abundance of envelope solutions,especially the solutions expressed by two different Jacobi elliptic functions,to the NLS equation have been obtained. Obviously,the extended F-expansion method can be applied to solve other type of nonlinear evolution equations as well.