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Title: Degenerate four-virtual-soliton resonance for the KP-II
Authors: Pashaev, Oktay
Francisco, Meltem L. Y.
Keywords: Ablowitz-Kaup-Newell-Segur hierarchy
Dissipative soliton
Hirota method
Kadomtsev-Petviashvili equation
Reaction-diffusion system
Soliton resonance
Issue Date: Jul-2005
Publisher: Pleiades Publishing
Source: Pashaev, O., and Francisco, M. L. Y. (2005). Degenerate four-virtual-soliton resonance for the KP-II. Theoretical and Mathematical Physics, 144(1), 1022-1029. doi:10.1007/s11232-005-0130-x
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,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
ISSN: 0040-5779
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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