Dissipative hierarchies and resonance solitons for KP-II and MKP-II
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CitationFrancisco, M. L. Y., Lee, J. H., and Pashaev, O. (2007). Dissipative hierarchies and resonance solitons for KP-II and MKP-II. Mathematics and Computers in Simulation, 74(4-5), 323-332. doi:10.1016/j.matcom.2006.10.017
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.