变系数非线性Schr?dinger方程的新精确解  

New Exact Solution to the Variable Coefficient Nonlinear Schr?dinger Equation

作　　者：杜玲禧 孙峪怀[1] 吴大山 DU Lingxi;SUN Yuhuai;WU Dashan(School of Mathematical Sciences,Sichuan Normal University,Chengdu,Sichuan 610066,China)

机构地区：[1]四川师范大学数学科学学院

出　　处：《内江师范学院学报》2019年第12期21-26,共6页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目（11371267）;四川省教育厅自然科学重点基金资助项目(2012ZA135)

摘　　要：首先对变系数Schrodinger方程进行行波变换转化为常微分方程,分离实部和虚部并分别令为零.由实部得到的第一种椭圆方程求得方程的冲击波解与包络孤波解,再利用(g′/g^2)-展开法,求得了一系列带参数的精确行波通解,其中包括有理函数解,三角函数解和双曲函数解.最后当参数取特殊值时进一步得到扭结波,周期波,孤立波等.Firstly the variable coefficient nonlinear Schrodinger equation was converted into an ordinary differential equation by means of travelling wave transformation.Then the real part was separated from the imaginary part and both parts were made to be zero.The shock wave solution and envelope solitary wave solution were obtained via the first type of elliptic equation derived from the real part.Then the exact traveling wave general solutions were determined using the g′/g^2-expansion method.The results include rational function solution,trigonometric function solution and hyperbolic function solution.When the parameter takes a special value,the kink wave solution,periodic wave solution and solitary wave solution can be worked out.

关 键 词：(g′/g^2)-展开法 变系数非线性Schrodinger方程 精确解 

分 类 号：O175.29[理学—数学]