Dissipative hierarchies and resonance solitons for KP-II and MKP-II
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.
Year of publication: |
2007
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Authors: | Francisco, Meltem L.Y. ; Lee, Jyh-Hao ; Pashaev, Oktay K. |
Published in: |
Mathematics and Computers in Simulation (MATCOM). - Elsevier, ISSN 0378-4754. - Vol. 74.2007, 4, p. 323-332
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Publisher: |
Elsevier |
Subject: | Dissipative hierarchies | Resonance solitons | Kadomtsev–Petviashvili equation | Hirota Method |
Saved in:
Online Resource
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