一类带强色散项DGH方程的精确解  

Exact Solutions of DGH Equation with Strong Dispersive Term

作　　者：蔡国梁[1] 王庆超[1] 凌旭东[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《大学数学》2008年第2期121-127,共7页College Mathematics

基　　金：国家自然科学基金项目(90210004;70571030);江苏大学高级人才基金项目(07JDG054)

摘　　要：利用改进的F-展开法,求出了一类带强色散项DGH方程的一系列类孤子解,三角函数周期解和有理数解,方程结合了KdV方程的线性色散项和C-H方程的非线性色散项.而且改进的F-展开法在借助于计算机符号系统Mathematica(Maple)下,操作方便,适用于大量的非线性偏微分方程(组),并有助于发现新解.By using a modified F-expansion method, rich families of exact solutions of DGH equation with strong dispersive term have been obtained, including soliton-like solutions, trigonometric function solutions and rational solutions. The equation combines the linear dispersion of Korteweg-de Veris equation with the nonlinear dipersion of the Camassa-Holm equation. With the aid of computer symbolic systems （Mathematica or Maple）, the method can be conveniently operated. Furthermore, the method can be applied to solve massive nonlinear PDEs（group）, as well as helps us find new exact solutions.

关 键 词：改进的F-展开法 DGH方程 RICCATI方程 精确解 

分 类 号：O175.2[理学—数学]