The Kadomtsev-Petviashvili Equation: the Trace Method and the Soliton Resonances

Abstract

The trace method which has been proposed by one of the authors (M.W.) and Sawada is applied to the Kadomtsev-Petviashvili equation with negative dispersion. The N-soliton solution and the Gelfand-Levitan equation are derived through the trace method. Soliton resonances are studied. It is found that the soliton resonance occurs when a virtual soliton in soliton solution turns into exact 1-soliton. Furthermore some interesting examples of soliton resonance related to 3-soliton solution are pointed out.