Soliton solutions of the Kadomtsev-Petviashvili II equation

Abstract

We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to the previously known line soliton solutions of KPII, this class also contains a large variety of multisoliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general, such solutions consist of unequal numbers of incoming and outgoing line solitons. From the asymptotic analysis of the tau function, we explicitly characterize the incoming and outgoing line solitons of this class of solutions. We illustrate these results by discussing several examples.