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arXiv · 1307.2976

Short-wave transverse instabilities of line solitons of the 2-D hyperbolic nonlinear Schr\"odinger equation

D. E. Pelinovsky·E. A. Ruvinskaya·O. A. Kurkina·B. Deconinck
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Abstract

We prove that line solitons of the two-dimensional hyperbolic nonlinear Schr\"odinger equation are unstable with respect to transverse perturbations of arbitrarily small periods, {\em i.e.}, short waves. The analysis is based on the construction of Jost functions for the continuous spectrum of Schr\"{o}dinger operators, the Sommerfeld radiation conditions, and the Lyapunov--Schmidt decomposition. Precise asymptotic expressions for the instability growth rate are derived in the limit of short periods.

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D. E. Pelinovsky, E. A. Ruvinskaya, O. A. Kurkina, B. Deconinck. 2013-07-11. Short-wave transverse instabilities of line solitons of the 2-D hyperbolic nonlinear Schr\"odinger equation. https://doi.org/10.1007/s11232-014-0154-1

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