Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2 1)-dimensional Kadomtsev-Petviashvili equation
Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2 1)-dimensional Kadomtsev-Petviashvili equation
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(2 1) 维 KadomtsevâPetviashvili 方程中块体与线波、块体波和呼吸波碰撞前后的轨迹方程
DOI：
10.1088/1674-1056/ab44a3
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发表时间：
2019
影响因子：
1.7
通讯作者：
Li Biao
中科院分区：
文献类型：
--
作者：
Zhang Zhao;Yang Xiangyu;Li Wentao;Li Biao
基于(2+1)维Kadomtsev-Petviashvili(KP)方程的混合解，进一步研究了KP方程解的运动轨迹。通过对KP方程的解在无限远的平行轨道上进行近似，得到了单个块体与直线波、块体和呼吸波碰撞前后的轨迹方程。我们推导了块波碰撞前后相变的数学表达式。同时，给出了一些碰撞图，揭示了明显的相变。我们提出的求解集总波轨迹方程的方法也适用于其他(2+1)维可积方程。这些结果扩展了对孤子理论中的块解、呼吸解和混合解的理解。
Based on the hybrid solutions to (2+ 1)-dimensional Kadomtsev–Petviashvili (KP) equation, the motion trajectory of the solutions to KP equation is further studied. We obtain trajectory equation of a single lump before and after collision with line, lump, and breather waves by approximating solutions of KP equation along some parallel orbits at infinity. We derive the mathematical expression of the phase change before and after the collision of a lump wave. At the same time, we give some collision plots to reveal the obvious phase change. Our method proposed to find the trajectory equation of a lump wave can be applied to other (2+ 1)-dimensional integrable equations. The results expand the understanding of lump, breather, and hybrid solutions in soliton theory.