基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解  

Traveling Wave Solutions to the Davey-Stewartson Equation With the Riccati-Bernoulli Sub-ODE Method

作　　者：杨小锋[1] 邓子辰[2] 魏乙[1] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]西北工业大学工程力学系,西安710072

出　　处：《应用数学和力学》2015年第10期1067-1075,共9页Applied Mathematics and Mechanics

基　　金：高校博士点基金(20126102110023);中央高校基本科研业务费专项资金(3102014JCQ01035)

摘　　要：Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程,再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组,求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法,得到了该方程的精确行波解.同时也得到了该方程的一个Bcklund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法.The Riccati-Bernonlli subsidiary ordinary differential equation （sub-ODE） method was proposed to construct the exact traveling wave solutions to the nonlinear partial differential equations （NLPDEs）. Through traveling wave transformation, the NLPDE was reduced to a nonlinear ODE. With the aid of the Riccati-Bernoulli sub-ODE, the nonlinear ODE was conver- ted into a set of nonlinear algebraic equations. The exact traveling wave solutions to the NLPDE were obtained as soon as this set of nonlinear algebraic equations were solved. Application of this method to the Davey-Stewartson equation directly gave the exact traveling wave solutions. The Backlund transformation of the Davey-Stewartson equation was also given. The results were compared with those of the first-integral method. The proposed method is effective and easy to be generalized to deal with other types of nonlinear partial differential equations.

关 键 词：Riccati—Bernoulli辅助常微分方程方法 Davey—Stewartson方程 行波解 BACKLUND变换 

分 类 号：O175.2[理学—数学]