一类非线性发展方程的显式精确解  

Explicit Exact Solutions to a Class of Nonlinear Evolution Equations

作　　者：陈自高[1] 

机构地区：[1]华北水利水电学院数学与信息科学学院,河南郑州450011

出　　处：《数学的实践与认识》2013年第9期201-207,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11101145);河南省科技厅自然科学基金(102102210216)

摘　　要：提出了寻求非线性发展方程行波解新的辅助方程法,作为实例通过选取变系数Bernoulli方程作为辅助常微分方程,并借助于计算机系统Mathematica和齐次平衡原则,求解了一类非线性发展方程,得到了该方程的新的显式精确解.所用方法可应用到其它类似方程的求解.A new auxiliaxy equation method for seeking traveling wave solutions to nonlinear evolution equations was proposed. As an example the Bernoulli equation with variable coef- ficient is chosen as auxiliary ordinary differential equation, with the help of computer system Mathematica and homogeneous balance principle, some new explicit exact solutions for a class of nonlinear evolution equations were obtained. The method used here could be applied to solve other similar equations.

关 键 词：变系数 辅助方程法 齐次平衡原则 行波解 

分 类 号：O175.29[理学—数学]