具波动算子的非线性Schrdinger方程的显式精确解  

Explicit and Exact Solutions for Nonlinear Schrdinger Equation with Wave Operator

作　　者：林成龙[1] 梁宗旗[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2017年第1期67-72,共6页Journal of Jimei University：Natural Science

基　　金：国家自然科学基金资助项目(11201178);福建省科技计划重点项目(2014H0034);福建省自然科学基金资助项目(2012J01013;2016J01310)

摘　　要：研究了具有波动算子的非线性Schrdinger方程显式精确解问题。先借助于一个规范行波变化,将该方程转化为微分方程动力系统,求出其奇点并给出其类型;采用直接积分法在特殊情况下得到该方程的一组显式精确解;最后利用预设Jacobi椭圆函数构造方法,得到了该方程多种形式的新的显式精确解。In this paper, the explicit and exact solutions for a class of nonlinear Schrodinger equation with wave operator were studied. With the help of a specific travelling wave transformation, the equation was transformed into a dynamic differential system, its singularity was obtained and its type was given. A set of explicit exact solutions of the equation were obtained by the direct integral method in special cases. Finally, the new forms of explicit and exact solutions of the equation were obtained by using the preset Jacobi elliptic function method.

关 键 词：波动算子 非线性SCHRODINGER方程 奇点 JACOBI椭圆函数 精确解 

分 类 号：O241.8[理学—计算数学]