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

作　　者：曹娜[1] 徐丽阳 尹晓军[1] CAO Na;XU Liyang;YIN Xiaojun(School of Science,Inner Mongolia Agricultural University,Hohhot 010018,China)

机构地区：[1]内蒙古农业大学理学院,内蒙古呼和浩特010018

出　　处：《应用数学》2023年第1期161-169,共9页Mathematica Applicata

基　　金：国家自然科学基金(11762011);内蒙古自然科学基金项目(2022QN01003);内蒙古自治区直属高校基本科研业务费项目(BR220126,22BR0902);内蒙古自治区高等学校科学研究项目(NJZY19045);内蒙古农业大学基础学科科研启动基金(JC2018003,JC2020003,JC2021001)。

摘　　要：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.

关 键 词：变系数F展开法 非线性SCHRODINGER方程 JACOBI椭圆函数解 

分 类 号：O175.2[理学—数学]