Geodesic
Short-wave transverse instabilities of line solitons of the~two-dimensional hyperbolic nonlinear Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 78-89

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We prove that line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation are unstable under transverse perturbations of arbitrarily small periods, i.e., short waves. The analysis is based on the construction of Jost functions for the continuous spectrum of Schrödinger operators, the Sommerfeld radiation conditions, and the Lyapunov–Schmidt decomposition. We derive precise asymptotic expressions for the instability growth rate in the limit of short periods.
Keywords: nonlinear Schrödinger equation, transverse instability, Lyapunov–Schmidt decomposition, Fermi's golden rule.
Mots-clés : soliton 
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     author = {D. E. Pelinovsky and E. A. Ruvinskaya and O. E. Kurkina and B. Deconinck},
     title = {Short-wave transverse instabilities of line solitons of the~two-dimensional hyperbolic nonlinear {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_179_1_a4/}
}
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D. E. Pelinovsky; E. A. Ruvinskaya; O. E. Kurkina; B. Deconinck. Short-wave transverse instabilities of line solitons of the~two-dimensional hyperbolic nonlinear Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 78-89. http://geodesic.mathdoc.fr/item/TMF_2014_179_1_a4/