Numerical study of the KP equation for non-periodic waves
Numerical study of the KP equation for non-periodic waves
复制标题
DOI：
10.1016/j.matcom.2010.05.025
复制
发表时间：
2010-04
期刊：
影响因子：
--
通讯作者：
C. Kao;Y. Kodama
中科院分区：
文献类型：
--
作者：
C. Kao;Y. Kodama
Kadomtsev-Petviashvili（KP）方程描述了在准二维情况下传播的弱色散和小振幅波。近年来，KP方程的精确孤子解被发现并被分类。这些孤子解在二维平面内沿沿着局域化，在其它位置指数衰减，本文称之为线孤子解。分类是基于远场图案的解决方案，其中包括一个有限数量的线孤子。本文用直接数值模拟的方法研究了由两个不同的线孤子组成的V形和X形初始波的KP方程的初值问题。然后，我们证明了该解决方案渐近收敛到其中一些精确的孤子解。收敛是局部定义的L2-意义。本文考虑的初始波型与浅水波问题中非线性波相互作用产生的无赖波有关。
The Kadomtsev–Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two-dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along certain lines in a two-dimensional plane and decay exponentially everywhere else, and they are called line-soliton solutions in this paper. The classification is based on the far-field patterns of the solutions which consist of a finite number of line-solitons. In this paper, we study the initial value problem of the KP equation with V- and X-shape initial waves consisting of two distinct line-solitons by means of the direct numerical simulation. We then show that the solution converges asymptotically to some of those exact soliton solutions. The convergence is in a locally defined L2-sense. The initial wave patterns considered in this paper are related to the rogue waves generated by nonlinear wave interactions in shallow water wave problem.