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改进的((G-G')/(G+G'))展开法及一类广义非线性Schrodinger方程的精确解研究
投稿时间:2019-08-09  修订日期:2019-12-08  点此下载全文
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作者单位E-mail
石兰芳 南京信息工程大学 shilf108@163.com 
王明灿 南京信息工程大学  
基金项目:国家自然科学基金项目;江苏省大学生创新创业训练计划
中文摘要:研究了改进的((G-G')/(G+G'))展开法,并应用这种方法得到广义非线性Schrodinger方程新形式的精确行波解,这些解包括三角函数解、双曲函数解、有理函数解和指数函数解。改进的((G-G')/(G+G'))展开法求解过程直接有效,所求解不仅覆盖了已知解,还包括一些全新的解,扩展了解的范围。这种方法还可以解决数学物理方程领域中的许多复杂非线性偏微分方程,具有广泛的应用价值。
中文关键词:改进的((G-G')/(G+G'))展开法  广义非线性Schrodinger方程  齐次平衡法  行波解  精确解
 
The modified ((G-G')/(G+G'))-expansion method and the study on the exact solutions of a class of the Generalized Nonlinear Schrodinger Equation
Abstract:The modified ((G-G')/(G+G'))-expansion method was successfully proposed to seek exact solutions of nonlinear partial differential equations and applied to solve the exact solutions of the Generalized nonlinear Schrodinger Equation. The solutions include hyperbolic function solutions, trigonometric function solutions, rational solutions as well as exponential function solutions. Being effective and straightforward, the method not only recovers some known solutions, but also finds some new solutions, which helps expand the scope of the solutions. Thus, the modified ((G-G')/(G+G'))-expansion method is of exactly great value and ready to solve more problems in mathematical physics.
keywords:The modified ((G-G')/(G+G'))-expansion method  exact solution  generalized nonlinear Schrodinger equation  homogeneous balance principle  travelling wave solutions.
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