This article is cited in 15 papers

Multi-component Wronskian solution to the Kadomtsev–Petviashvili equation

Tao Xu^a, Fu-Wei Sun^b, Yi Zhang^a, Juan Li<sup>cd

a</sup> College of Science, China University of Petroleum, Beijing 102249, China
^b College of Science, North China University of Technology Beijing 100041, China
^c Demonstration Centre, Spaceborne Remote Sensing National Space Administration, Beijing 100101, China
^d State Key Laboratory of Remote Sensing Science, Jointly Sponsored by the Institute of Remote Sensing Applications of Chinese of Sciences Academy and Beijing Normal University, Beijing 100101, China

Abstract: 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 non-linearization 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 $y\to\mp\infty$ 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.

Key words: Kadomtsev–Petviashvili equation, multi-component Wronskian, soliton solutions, Darboux transformation.

UDC: 519.634

Received: 14.01.2013

Language: English

DOI: 10.7868/S0044466914010165

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:1, 97–113

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