标题： 多组分Wronskian解到Kadomtsev-Petviashvili方程 显示英文标题

标题： Multi-component Wronskian solution to the Kadomtsev-Petviashvili equation

摘要： 已知Kadomtsev-Petviashvili（KP）方程可以通过Lax对的二元非线性化分解为耦合Ablowitz-Kaup-Newell-Segur（AKNS）层次的前两个成员。 在本文中，我们构建了二阶和三阶m耦合AKNS系统的N次迭代Darboux变换（DT）。 通过结合N次迭代DT和Cramer法则，我们发现KPII方程具有未约化的多分量Wronskian解，而KPI方程则接受一个约化的多分量Wronskian解。 特别是，基于未约化的和约化的两分量Wronskian，我们得到了两族完全共振的线孤子解，这些解在y->\mp \infty 时包含任意数量的渐近孤子，适用于KPII方程，并且得到了KPI方程的普通N孤子解。 此外，我们发现KPI线孤子在平行传播时，在碰撞瞬间可以表现出束缚态。 显示英文摘要

摘要： It is known that the Kadomtsev-Petviashvili (KP) equation can be decomposed into the first two members of the coupled Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy by the binary nonlinearization of Lax pairs. In this paper, we construct the N-th iterated Darboux transformation (DT) for the second- and third-order m-coupled AKNS systems. By using together the N-th iterated DT and Cramer's rule, we find that the KPII equation has the unreduced multi-component Wronskian solution and the KPI equation admits a reduced multi-component Wronskian solution. In particular, based on the unreduced and reduced two-component Wronskians, we obtain two families of fully-resonant line-soliton solutions which contain arbitrary numbers of asymptotic solitons as y->\mp\infty to the KPII equation, and the ordinary N-soliton solution to the KPI equation. In addition, we find that the KPI line solitons propagating in parallel can exhibit the bound state at the moment of collision.