b-方程类的二类行波解  

Two types traveling wave solutions for b-equation

作　　者：余丽琴[1] 田立新[1] 

机构地区：[1]江苏大学非线性科学研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2005年第B12期15-19,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10071033);江苏省自然科学基金资助项目(BK2002003)

摘　　要：研究了非线性偏微分b-方程类在两种情况下的精确行波解.首先在b=3,c=1时,对于有色散项的Degasperis-Procesi方程,根据它所对应的行波系统,利用R iccati方程有更多新解的特点,借助Mathematica软件,采用齐次平衡法构造了该方程的一些具有双曲正切函数形式的多孤子解和三角周期解.其次用积分的方法研究了b-方程类在b=2c情况下的行波解,并用数值模拟的方法给出了部分尖峰孤波解的图形.Exact traveling wave solutions are investigated for the b-equation under two cases. Firstly, for the case b = 3 and c = 1 ,for the Degasperis-Procesi equation with the dispersion term, by considering its traveling wave system, and taking full advantage of the Riccati equation which has more new solution, homogeneous balance method is used to construct more new multiple soliton and triangle periodic solutions with tanh function form for this equation with the aid of Mathematica. Secondly, the integral method is employed to investigate the equation corresponding to the b-equation for the case b = 2c, Numerical simulation is used to give the graph of some peaked solitary wave solutions.

关 键 词：偏微分方程 b-方程类 DEGASPERIS-PROCESI方程 齐次平衡法 行波解 孤波解 

分 类 号：O175.14[理学—数学]