一类具波动算子非线性Schr?dinger方程的精确解  

Exact solutions for a class of nonlinear Schr?dinger equation with wave operator

作　　者：林成龙 梁宗旗[2] LIN Chenglong;LIANG Zongqi(School of Economics and Management,Nanjing University of Science and Technology,Nanjing 210094,China;School of Science,Jimei University,Xiamen 361021,Fujian Province,China)

机构地区：[1]南京理工大学经济管理学院,南京210094 [2]集美大学理学院,福建厦门361021

出　　处：《应用数学与计算数学学报》2018年第4期867-878,共12页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11801214);福建省高校产学研科技资助项目(2017H6015);福建省自然科学基金资助项目(2016J01310,2017J01402,2017J01557,JZ160450)

摘　　要：研究一类具波动算子非线性Schr?dinger方程的精确解问题.引入Jacobi椭圆函数组合及双曲函数组合方法,将其应用于求解具有波动算子的非线性Schr?dinger方程中.通过简单代数运算,可以得到具有波动算子非线性Schr?dinger方程的许多新解,并在极限情况下,给出了该方程对应的双曲函数解.同时得出了双曲函数组合解是Jacobi椭圆函数组合解情况下的极限解的结论.该方法可以推广到更多非线性偏微分方程精确解求解问题.In this paper,exact solutions for a class of nonlinear Schr¨odinger equation with wave operator are studied.The Jacobi elliptic function and the hyperbolic function combination method are involved in order to obtain the exact solutions.Many new solutions of the nonlinear Schrodinger equation with wave operator are obtained by the simple algebraic operation and the corresponding hyperbolic function solution of equation in the limit case.Meanwhile,the conclusion is drawn that combination solutions of the hyperbolic function are the limit situation of combination solutions of the Jacobi elliptic function.This method can be applied to solving more nonlinear partial differential equations.

关 键 词：非线性Schro DINGER方程 波动算子 JACOBI椭圆函数 双曲函数 精确解 

分 类 号：O241.8[理学—计算数学]