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arXiv · hep-th/0410032

Soliton Resonances for MKP-II

Jyh-Hao Lee·Oktay K. Pashaev
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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.

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Jyh-Hao Lee, Oktay K. Pashaev. 2004-10-04. Soliton Resonances for MKP-II. https://doi.org/10.1007/s11232-005-0127-5

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