(2+1)维Korteweg-de Vries方程的复合波解及局域激发

Complex wave solutions and localized excitations of (2+1)-dimensional korteweg-de Vries system

借助 Maple 符号计算软件,利用 Riccati 方程（ξ′= a0＋a1ξ＋a2ξ2）展开法和变量分离法,得到了（2＋1）维Korteweg-de Vries方程（KdV）包含q=C1x＋C2y＋C3t＋R（x, y, t）的复合波解。根据得到的孤立波解,构造出KdV方程新颖的复合波裂变和复合波湮灭等局域激发结构。

With the help of the symbolic computation system Maple and Riccati equation （ξ′ =a0＋a1ξ＋a2ξ2） expansion method and a variable separation method, some complex wave solutions with q = C1x＋C2y＋C3t＋R（x, y, t） of the （2＋1）-dimensional Korteweg-de Vries system is derived. Based on the derived solitary wave solution, some novel complex wave localized excitations such as complex wave fusion and complex wave annihilation are investigated.