Vandermonde-like determinants’ representations of Darboux transformations and explicit solutions for the modified Kadomtsev–Petviashvili equation

Ding-jiang Huang and Hong-qing Zhang

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 18, 4565-4580

Abstract: Recently, the (2+1)-dimensional modified Kadomtsev–Petviashvili (mKP) equation was decomposed into two known (1+1)-dimensional soliton equations by Dai and Geng [H.H. Dai, X.G. Geng, J. Math. Phys. 41 (2000) 7501]. In the present paper, a systematic and simple method is proposed for constructing three kinds of explicit N-fold Darboux transformations and their Vandermonde-like determinants’ representations of the two known (1+1)-dimensional soliton equations based on their Lax pairs. As an application of the Darboux transformations, three explicit multi-soliton solutions of the two (1+1)-dimensional soliton equations are obtained; in particular six new explicit soliton solutions of the (2+1)-dimensional mKP equation are presented by using the decomposition. The explicit formulas of all the soliton solutions are also expressed by Vandermonde-like determinants which are remarkably compact and transparent.

Keywords: N-fold Darboux transformations; Explicit solutions; Vandermonde-like determinants; Soliton equation; mKP equation (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:18:p:4565-4580

DOI: 10.1016/j.physa.2008.03.020

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