The homotopic mapping solutions for the generalized Schr?dinger equation

3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015

数学;化学;物理学

Lu, Dianhen^1 ; Cui, Xinyu^1 ; Hong, Baojian^1

Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang Jiangsu

212013, China^1

关键词: Approximation solution;    Auxiliary functions;    Dinger equation;    Exact solution;    Hirota equation;    Homotopic;    Homotopic mapping;    Initial conditions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/622/1/012043/pdf
DOI  :  10.1088/1742-6596/622/1/012043

来源: IOP

【 摘 要 】

This work is concerned on how to find the approximation solutions of the generalized Schrödinger equation by using the homotopic mapping method. First, we give the basic idea of Homotopic mapping method. In the following, we introduce a homotopic mapping, and make the generalized Schrödinger equation do a homotopic deformation, then we get the approximation solutions in given initial conditions. Finally we give two examples about derivative Schrödinger equation and Hirota equation to illustrate efficiency of this method, and the exact solutions of these equations can be solved in the condition of selecting proper auxiliary function v.