D. E. Pelinovsky, E. A. Ruvinskaya, O. E. Kurkina, B. Deconinck, “Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation”, TMF, 2014, Volume 179, Number 1,Pages <nobr>78

This article is cited in 13 papers

Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation

D. E. Pelinovsky^ab, E. A. Ruvinskaya^a, O. E. Kurkina^ac, B. Deconinck^d

^a Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
^b Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
^c Higher School of Economics, Nizhny Novgorod, Russia
^d Department of Applied Mathematics, University of Washington, Seattle, WA, USA

Abstract: 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, soliton, transverse instability, Lyapunov–Schmidt decomposition, Fermi's golden rule.

Received: 24.06.2013

DOI: 10.4213/tmf8568