This article is cited in 17 papers

Degenerate Four-Virtual-Soliton Resonance for the KP-II

O. K. Pashaev, L. Y. Francisco

Izmir Institute of Technology

Abstract: We propose a method for solving the $(2+1)$-dimensional Kadomtsev–Petviashvili equation with negative dispersion (KP-II) using the second and third members of the disipative version of the AKNS hierarchy. We show that dissipative solitons (dissipatons) of those members yield the planar solitons of the KP-II. From the Hirota bilinear form of the $SL(2,\mathbb R)$ AKNS flows, we formulate a new bilinear representation for the KP-II, by which we construct one- and two-soliton solutions and study the resonance character of their mutual interactions. Using our bilinear form, for the first time, we create a four-virtual-soliton resonance solution of the KP-II, and we show that it can be obtained as a reduction of a four-soliton solution in the Hirota–Satsuma bilinear form for the KP-II.

Keywords: dissipative soliton, Ablowitz–Kaup–Newell–Segur hierarchy, Kadomtsev–Petviashvili equation, Hirota method, soliton resonance, reaction-diffusion system.

DOI: 10.4213/tmf1842

 English version: Theoretical and Mathematical Physics, 2005, 144:1, 1022–1029

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