一类变式Boussinesq系统的行波解  

Travelling Wave Solutions of a Variant of the Boussinesq System

作　　者：邓圣福[1] 郭柏灵[2] 

机构地区：[1]湛江师范学院数学与计算科学学院,湛江524048 [2]北京应用物理与计算数学研究所,北京100088

出　　处：《应用数学学报》2012年第6期1099-1112,共14页Acta Mathematicae Applicatae Sinica

基　　金：教育部留学回国人员科研启动基金((2012)940);广东省自然科学基金博士启动(S2011040000464);广东省高等学校科技创新(2012KJCX0074);湛江师范学院博士专项基金(ZL1101)资助项目

摘　　要：本文研究一类变式Boussinesq系统η_t+((1+αη)w)_x-β/6w_(xxx)=0,w_t+αww_x+η_x-β/2w_(xxt)=0,其中α和β都是正常数.许多逼近模型都能从此系统中被推导出,比如Boussinesq系统和两分量Camassa-Holm系统等.本文利用平面动力系统方法研究它的行波解及相图,得到了孤立波解,广义扭波解,广义反扭波解,紧孤立波解和周期波解,并给出了这些解的数值模拟.This paper considers a variant of the Boussinesq system ηt＋（1＋αη）ω）x-β/6ωxxx=0,ωt＋αωωx＋β/2ωxxt=0, where α and β are positive constants. A lot of approximate moadls llKe the Doussinesq system and the two-component Camassa-Holm system can be derived from this system. We here study its travelling wave solutions and analyze its phase portraits by applying the qualitative analysis methods of planar autonomous systems. We obtain its solitary wave solutions, kink-like or antikink-like wave solutions, compacton-like wave solutions and periodic wave solutions. Some numerical simulations of its solutions are also given.

关 键 词：孤立波解 广义(反)扭波解 紧孤立波解 周期波解 

分 类 号：O175.12[理学—数学]