Degenerate Four Virtual Soliton Resonance for KP-II

Abstract

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional Kadomtsev-Petviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by which, one and two soliton solutions are constructed and the resonance character of their mutual interactions is studied. By our bilinear form, 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.

10 pages, 5 figures, Talk on International Conference Nonlinear Physics. Theory and Experiment. III, 24 June-3 July, 2004, Gallipoli(Lecce), Italy

References in corpus (2)

• Young diagrams and N-soliton solutions of the KP equation
• Soliton Resonances for MKP-II

Cited by in corpus (8)

• Soliton solutions of the Kadomtsev-Petviashvili II equation
• Young diagrams and N-soliton solutions of the KP equation
• Classification of the line-soliton solutions of KPII
• A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation
• On the construction of the KP line-solitons and their interactions
• Soliton Resonances for MKP-II
• Localized stem structures in soliton reconnection of the asymmetric Nizhnik-Novikov-Veselov system
• Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation