On the construction of the KP line-solitons and their interactions

Abstract

The line-soliton solutions of the Kadomtsev–Petviashvili (KP) equation are investigated in this article using the τ-function formalism. In particular, the Wronskian and the Grammian forms of the τ-function are discussed, and the equivalence of these two forms are established. Furthermore, the interaction properties of two special types of 2-soliton solutions of the KP equation are studied in details.

Keywords:

• KP equation
• line-solitons
• τ-function

AMS Subject Classifications:

• 37K10
• 37K35
• 37K40

Acknowledgements

We thank Yuji Kodama for useful discussions. The research of the S. Chakravarty and T. Lewkow is partially supported by the NSF grant DMS-0807404.