广义对称正则长波方程的显式精确解析解  

Explicit and exact analytic solutions to generalized symmetric regularized long wave equations

作　　者：尚亚东[1] 

机构地区：[1]广州大学理学院,广东广州510405

出　　处：《广州大学学报（自然科学版）》2003年第2期101-105,共5页Journal of Guangzhou University:Natural Science Edition

摘　　要：首先对具耗散项的广义对称正则长波方程utt-uxx-γuxxt-uxxtt+f(u) xt=0 ,(γ≠ 0 )的孤立波解建立了一个关系式 .据此推知 :具耗散项的广义对称正则长波方程不可能有钟状孤立波解 ,而只可能有扭状孤立波解或钟状扭状复合型孤立波解 .广义对称正则长波方程utt-uxx-uxxtt+f(u) xt=0可能既有钟状孤立波解 ,又有扭状孤立波解 .进而求出了上述两个方程的显式精确孤立波解。Firstly, we establish a formula satisfied by the solitary wave solutions of the generalized symmetric regularized long wave equation with dissipation term u tt -u xx -γ u xxt -u xxtt +f(u) xt =0 . It is shown that the generalized symmetric regularized long wave equation with dissipation term has not bell profile solitary wave solutions but may have kink profile solitary wave equations or solitary wave solutions of a kind of the compound bell_type with kink_type.However, the generalized symmetric regularized long wave equation u tt -u xx -u xxtt +f(u) xt =0 may have not only bell profile solitary wave solutions but also kink profile solitary wave solutions. Furthermore, all expected solitary wave solutions, singular travelling wave solutions and periodic wave solutions of triangular function type are obtained.

关 键 词：广义对称正则长波方程 显式精确解析解 耗散项 孤立波解 奇异行波解 三角函数状周期波解 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]