Geodesic
Degenerate Four-Virtual-Soliton Resonance for the KP-II
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 162-170

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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.
Mots-clés : dissipative soliton, reaction-diffusion system.
Keywords: Ablowitz–Kaup–Newell–Segur hierarchy, Kadomtsev–Petviashvili equation, Hirota method, soliton resonance 
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     author = {O. K. Pashaev and L. Y. Francisco},
     title = {Degenerate {Four-Virtual-Soliton} {Resonance} for the {KP-II}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {162--170},
     publisher = {mathdoc},
     volume = {144},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a16/}
}
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O. K. Pashaev; L. Y. Francisco. Degenerate Four-Virtual-Soliton Resonance for the KP-II. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 162-170. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a16/