三阶非线性项的耦合标量场方程的精确孤子解  

Exact soliton solutions for third-order nonlinear coupled scalar field equation

作　　者：柴岩[1] 

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《辽宁工程技术大学学报（自然科学版）》2010年第4期697-700,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家高技术研究发展"863"计划基金资助项目(2002AA420060)

摘　　要：针对非线性耦合标量场方程的求解问题,采用改进的sine-cosine法,并把它应用到n+1维耦合非线性标量场方程,同时利用Mathematica数学软件并结合吴文俊消元法,获得了n+1维耦合标量场方程的5类精确孤子解,部分已知的结论是其特例;该方法还能够有效地用于其他的非线性方程组,如耦合Kdv方程、耦合mkdv方程、耦合schr(o|¨)dinger和Boussinesq方程及正则长水波方程等.Based on the solution of the nonlinear coupled scalar field, this paper obtains five types of exact soliton solutions for （n＋1） dimensional coupled scalar field equation by using an improved method of Sine-Cosine and applying it to the （n＋1） dimension of nonlinear coupled scalar field equations, and at the same time, using mathematical Mathematica software and Wu-elimination. The known conclusions are only special cases. The method can be used effectively in other nonlinear equations, such as the coupled .KdV equation, coupled mKdV equation, coupled Schrǒdinger and Boussinesq equation, and coupled regular long wave equation.

关 键 词：耦合标量场方程 sine-cosine法 吴文俊消元法 精确孤子解 

分 类 号：O175[理学—数学]