变系数F展开法求解非线性Schrodinger方程的精确解

Exact Solutions of Nonlinear Schrodinger Equation by Variable-coefficient F-expansion Method

本文基于变系数F展开法,并借助Mathematica数学软件,求解了水平科氏力作用下Rossby波振幅满足的非线性Schrodinger方程,得到一系列Jacobi椭圆函数解,以及当模数m→1和m→0时由其退化的双曲函数解和三角函数解,并绘制它们的三维图形.扩展了变系数F展开法求解非线性偏微分方程的应用范畴.同时也为非线性Schr?dinger方程得到更多形式的精确解.

This paper uses the variable-coefficient F-expansion method and mathematical software Mathematica to solve the nonlinear Schrodinger equation,which meets the requirement of the Rossby wave amplitude under the action of horizontal Coriolis force.It also gets a series of solutions of Jacobi elliptic function,and the solutions of hyperbolic function and trigonometric function are degenerated by solutions of Jacobi elliptic function when modulus m→1 and m→0,and even draw the 3 D graphics.This paper extends the application of the variable-coefficient F-expansion method to solve the nonlinear partial differential equations,and also gets more forms of exact solutions for nonlinear Schr?dinger equation.