Soliton Resonances for MKP-II
Abstract
Using the second flow - the Derivative Reaction-Diffusion system, and the third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the product of two functions, satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative dispersion (MKP-II). We construct Hirota's bilinear representation for both flows and combine them together as the bilinear system for MKP-II. Using this bilinear form we find one and two soliton solutions for the MKP-II. For special values of parameters our solution shows resonance behaviour with creation of four virtual solitons. Our approach allows one to interpret the resonance soliton as a composite object of two dissipative solitons in 1+1 dimensions.
Keywords
Cite
@article{arxiv.hep-th/0410032,
title = {Soliton Resonances for MKP-II},
author = {Jyh-Hao Lee and Oktay K. Pashaev},
journal= {arXiv preprint arXiv:hep-th/0410032},
year = {2009}
}
Comments
11 pages, 2 figures, Talk on International Conference "Nonlinear Physics. Theory and Experiment. III", 24 June-3 July, 2004, Gallipoli(Lecce), Italy