应用Riccati-Bernoulli辅助方程求解广义非线性Schrodinger方程和(2+1)维非线性Ginzburg-Landau方程  

Solution of Generalized Nonlinear Schrodinger Equations and (2+1)-Dimensional Nonlinear Ginzburg-Landau Equations With a Riccati-Bernoulli Auxiliary Equation Method

作　　者：石兰芳[1] 王明灿 钱正雅 SHI Lanfang;WANG Mingcan;QIAN Zhengya(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,P.R.China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《应用数学和力学》2020年第7期786-795,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11202106,61201444);江苏省大学生创新创业训练计划(201810300204)。

摘　　要：研究了Riccati-Bernoulli辅助方程法,并应用这种方法得到广义非线性Schrodinger方程和(2+1)维非线性Ginzburg-Landau方程的精确行波解.这些解包括有理函数、三角函数、双曲函数和指数函数.应用这种方法求解过程简洁有效.该研究对于数学物理方程领域诸多非线性偏微分方程精确解的探究具有重要的意义.The Riccati-Bernoulli auxiliary equation method was proposed to seek the exact travelling solutions to the generalized nonlinear Schrodinger equation and the(2+1)-dimensional nonlinear Ginzburg-Landau equation. The solutions can be expressed with the rational functions, the trigonometric functions, the hyperbolic functions and the exponential functions. Being effective and concise, the method is important to obtain the exact travelling solutions for more nonlinear partial differential equations in the field of mathematics and physics.

关 键 词：Riccati-Bernoulli辅助方程法 广义非线性Schrodinger方程 (2+1)维非线性Ginzburg-Landau方程 行波解 

分 类 号：O175.29[理学—数学]