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Article

Коротковолновые поперечные неустойчивости плоских солитонов в двумерном гиперболическом нелинейном уравнении Шредингера

Пелиновский Д. Е., Рувинская Е. А., Куркина О. Е., Деконинк Б.
We prove that line solitons of the two-dimensional hyperbolic nonlinear Schr¨odinger 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 Schr¨odinger 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.