广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解  

Projective Riccati Equation Method and New Exact Travelling Wave Solutions for the (2+l)-dimensionaI Long Wave Equations

作　　者：智红燕[1] 陈勇[2] 张鸿庆[1] 

机构地区：[1]大连理工大学应用数学系,大连116024 [2]宁波大学数学系

出　　处：《数学物理学报（A辑）》2005年第S1期956-964,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(10072013)国家重点基础研究发展规划项目(G1998030600)中国博士后基金浙江省自然科学基金(Y604056)资助

摘　　要：助于符号计算软件Maple,通过一种构造非线性偏微分方程更一般形式行波解的直接方 法,即改进的广义射影Ricccati方程方法,求解(2+1)维色散长波方程,得到该方程的新的 更一般形式的行波解,包括扭状孤波解,钟状解,孤子解和周期解．并对部分新形式孤波解画 图示意．Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations (PDEs) and implemented in a computer algebraic system, the authors consider the (2+l)-dimensional dispersive long wave equations(DLWE). More and new general form solutions are obtained, including kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions. The properties of some new formal solitary wave solutions are shown by some figures.

关 键 词：广义射影Riccati方程方法 (2+1)维色散长波方程 行波解 

分 类 号：O175.29[理学—数学]