摘要
该文推导了具任意次非线性项的Liénard方程a″(ξ)+la(ξ)+maq(ξ)+na2q-1(ξ)=0和a″(ξ)+ra′(ξ)+la(ξ)+maq(ξ)+na2q-1(ξ)=0解的若干性质,通过适当变换,并结合假设待定法求出了它们的钟状和扭状显式精确解.据此,求出了一批具任意次非线性项的发展方程的钟状和扭状显式精确孤波解,其中包括广义BBM型方程、二维广义Klein-Gordon方程、广义Pochhammer-Chree方程和非线性波方程等.
In this paper, the authors first establish some properties of solutions for Liénard equation with nonlinear terms of any order. Then, explicit exact solutions for the Liénard equation are obtained by proper transformation and undetermined assumption method. By means of these solutions, the authors obtain explicit exact bell and kink profile solitary wave solutions for many nonlinear evolution equation with nonlinear terms of any degree. These nonlinear equations include generalized BBM type, generalized Klein-Gordon, generalized Pochhammer-Chree and generalized wave equation.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2005年第1期119-129,共11页
Acta Mathematica Scientia
基金
国家自然科学基金(10371023)
上海市科技发展基金(03ZR14070)资助
关键词
孤波
LIÉNARD方程
非线性发展方程
精确解
待定假设法
Solitary wave
Liénard equation
Nonlinear evolution equation exact solution
Undetermined assumption method.
