Number:         Mech 229/01
Author(s):       PETERSON, P.
Title:               Construction and decomposition of multi-soliton solutions of KdV type equations. 18 p.
Language:      English

ABSTRACT.   A detailed description of multi-soliton (more than two) interactions is needed for practical for many applications for solving both the direct and inverse problems in multi-directional wave phenomenon (for example, surface waves). In this paper a strict novel formalism for constructing multi-soliton solutions of KdV (Korteweg-de Vries) type 2-D equations is presented. In this formalism solutions are derived in phase variables, in which the analysis of multi-soliton interactions is most natural and simple. Results of this paper include (i) a complete description of KdV 2-D multi-soliton solutions based on the Hirota formalism, and (ii) a novel decomposition of multi-soliton solutions. With this decomposition a multi-soliton solution is interpreted as a linear superposition of solitons and interaction solitons. Finally, expressions for calculating the amplitudes of interaction solitons are derived.

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  MT   17.02.2003