Soliton solutions of the Kadomtsev-Petviashvili II equation

Details Soliton solutions of the Kadomtsev-Petviashvili II equation Soliton solutions of the Kadomtsev-Petviashvili II equation

2005-11-30

arxiv.org/abs/nlin/0511068v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

28 pages, 4 figures

Scientific paper

10.1063/1.2181907

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 previously known line-soliton solutions, this class also contains a large variety of new multi-soliton 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.

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