Degasperis-Procesi方程的一类新的行波解  

New traveling wave solution for Degasperis-Procesi 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3期231-234,共4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：利用齐次平衡法,研究了非线性偏微分Degasperis-Procesi方程的行波解.根据DegasperisProcesi方程所对应的行波系统,利用Riccati方程有更多新解的特点,借助Mathematica软件,构造了Degasperis-Procesi方程的一些具有正切函数形式的多孤子解和三角周期解,用数值模拟的方法给出了部分多孤子解和三角周期解的图形,从而表明了解的几何特征.这种方法也适用于其他的非线性方程.Homogeneous balance method is employed to investigate the traveling wave solution for the Degasperis-Procesi equation. For the traveling wave system corresponding to the Degasperis-Procesi equation, by taking full advantage of the Riccati equation which has more new solutions and by using the software of Mathematica, homogeneous balance method is used to construct more new multiple soliton and triangle periodic solutions with tanh function form for the Degasperis-Procesi equation. Numerical simulation is used to give the graph of some solutions, and to show the geometric properties of solution.

关 键 词：非线性偏微分方程 Degasperis—Procesi方程 齐次平衡法 行波解 孤立波解 

分 类 号：O175.14[理学—数学]