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

✍ Scribed by Meltem L.Y. Francisco; Jyh-Hao Lee; Oktay K. Pashaev

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 237 KB
• Volume: 74
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/j.matcom.2006.10.017

✦ Synopsis

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.