(2+1)维Broer-Kaup方程的精确孤子解

Exact soliton solutions of the (2+1)-dimensional Broer Kaup equation

利用 Backlund变换方法和截断 Painlevé分析方法研究了 ( 2 +1 )维 Broer-Kaup方程 .给出了许多有意义的精确孤立子解 .一类多孤子解可以借助于变换系数的扩散方程的精确解来述 .由于在孤子解的一般式中包含了 3个任意函数 ,使 ( 2 +1 )维 Broer-Kaup方程具有非常丰富的孤子结构 .当这些任意函数被适当选定时 ,可以得到多直线孤子和多曲线孤子解 。

By means of the Bcklund transformation and the standard truncated Painlevé analysis ,many significant excat soliton solutions of the (2+1) dimensional Broer Kaup equation were obtained.A special type of soliton solutions could be described by the variable coefficient heat conduction equation.The entrance of three arbitrary functions in the general expressions of the soliton made the solitons of the (2+1) dimensional Broer Kaup equation posses abundant structures.By fixing the arbitary functions appropriately,it was proved multiple straight line solitons,multiple straight line solitons,dromions,ring solitons and so on.