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This article is cited in 16 scientific papers (total in 16 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.
Citation:
O. K. Pashaev, L. Y. Francisco, “Degenerate Four-Virtual-Soliton Resonance for the KP-II”, TMF, 144:1 (2005), 162–170; Theoret. and Math. Phys., 144:1 (2005), 1022–1029
Linking options:
https://www.mathnet.ru/eng/tmf1842https://doi.org/10.4213/tmf1842 https://www.mathnet.ru/eng/tmf/v144/i1/p162
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Abstract page: | 374 | Full-text PDF : | 201 | References: | 80 | First page: | 1 |
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