非线性耦合标量场方程新的精确行波解  

New Exact Solutions to the Nonlinear Coupled Scalar Field Equations

作　　者：杜兴华[1] 

机构地区：[1]大庆石油学院数学系,黑龙江大庆163318

出　　处：《数学的实践与认识》2007年第6期153-159,共7页Mathematics in Practice and Theory

摘　　要：对于具有丰富物理意义和众多应用价值的非线性耦合标量场方程,通过将所求方程约化为初等积分形式,再利用多项完全判别系统对被积函数中的多项式的根进行分类,得到该方程的丰富的精确解,其中包含有理函数型解,孤波解,三角函数型周期解,椭圆函数型周期解,这其中有许多是新解.这一方法是非常简洁而又有力的,对于椭圆方程,它能得到所有可能的解,对于更高阶方程,与其它方法相比,多项式完全判别系统方法是更有力的.Considered the nonlinear coupled scalar field equation, reduced it to nonlinear ordinary differential equation with elementary integral form. According to a complete discrimination system for polynomial, one can classify the roots of respective polynomial to solve the respective elementary integral. Abundant solutions for the equation considered were obtained, which included many new solutions. This method can be applied to many similar problems.

关 键 词：多项式完全判别系统 非线性耦合标量场方程 孤波解 周期解 

分 类 号：O175.29[理学—数学]