Geodesic
Soliton Resonances for the MKP-II
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 133-142

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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 
@article{TMF_2005_144_1_a13,
     author = {J.-H. Lee and O. K. Pashaev},
     title = {Soliton {Resonances} for the {MKP-II}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {133--142},
     publisher = {mathdoc},
     volume = {144},
     number = {1},
     year = {2005},
     language = {ru},
     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/