非线性Schringer方程的Jacobi椭圆函数包络解

Jacobi elliptic function envelope solutions of nonlinear Schringer equation

通过函数变换和扩展Jacobi椭圆函数展开法,利用吴消元法,借助符号运算软件Maple,得到非线性Schringer方程丰富的包络形式精确解,特别是由两个Jacobi椭圆函数表示的精确解.当模数m→1或m→0时,一部分解退化为双曲函数或三角函数表示的解,F-展开法和扩展的F-展开法得到的精确解是本文结果的特例.

In this paper, by a function transformation and extended Jacobi elliptic function expansion method, using the Wu elimination method, getting Jacobi elliptic function envelope solutions of nonlinear Schroinger equation with the aid of computer algebra system Maple, especially some solutions are made up of two Jacobi elliptic functions, when the modulus m→1 or m→0 , a few corresponding hyperbolic function solutions or trigonometric function solutions are also obtained. The results of F - expansion method and extended F-expansion method are special cases of our results.