Dissipative hierarchies and resonance solitons for KP-II and MKP-II

Meltem L.Y. Francisco, Jyh-Hao Lee and Oktay K. Pashaev

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 74, issue 4, 323-332

Abstract: We show that dissipative solitons (dissipatons) of the second and the third members of SL(2,R) AKNS hierarchy give rise to the real solitons of KP-II, while for SL(2,R) Kaup-Newell hierarchy they give solitons of MKP-II. By the Hirota bilinear form for both flows, we find new bilinear system for these equations, and one- and two-soliton solutions. For special values of parameters our solutions show resonance behaviour with creation of four virtual solitons. We first time created four virtual soliton resonance solution for KP-II and established relations of it with degenerate four-soliton solution in the Hirota-Satsuma bilinear form for KP-II. Our approach allows one to interpret the resonance soliton as a composite object of two dissipative solitons in 1+1 dimensions.

Keywords: Dissipative hierarchies; Resonance solitons; Kadomtsev–Petviashvili equation; Hirota Method (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:74:y:2007:i:4:p:323-332

DOI: 10.1016/j.matcom.2006.10.017

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