Geodesic
Soliton Resonances for the MKP-II
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 133-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the second flow (derivative reaction-diffusion system) and the third one of the dissipative $SL(2,\mathbb R)$ Kaup–Newell hierarchy, we show that the product of two functions satisfying those systems is a solution of the modified Kadomtsev–Petviashvili equation in $2+1$ dimensions with negative dispersion (MKP-II). We construct Hirota's bilinear representations for both flows and combine them as the bilinear system for the MKP-II. Using this bilinear form, we find one- and two-soliton solutions for the MKP-II. For special values of the parameters, our solution shows resonance behavior with the creation of four virtual solitons. Our approach allows interpreting the resonance soliton as a composite object of two dissipative solitons in $1+1$ dimensions.
Keywords: soliton resonance, modified Kadomtsev–Petviashvili equation, Hirota method, derivative reaction-diffusion system.
Mots-clés : dissipative soliton 
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     title = {Soliton {Resonances} for the {MKP-II}},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a13/}
}
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J.-H. Lee; O. K. Pashaev. Soliton Resonances for the MKP-II. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 133-142. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a13/

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