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On the susceptibility of bright nonlinear Schrödinger solitons to long-wave transverse instability

Bridges, T. J. (2004) On the susceptibility of bright nonlinear Schrödinger solitons to long-wave transverse instability Proceedings of the Royal Society of London A, 460. pp. 2605-2615.

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Abstract

<p>A new theory for transverse instability of bright solitons of equations of nonlinear Schrödinger (NLS) type is presented, based on a natural deformation of the solitons into a four-parameter family. This deformation induces a set of four diagnostic functionals which encode information about transverse instability. These functionals include the deformed power, the deformed momentum and two new functionals. The main result is that a sufficient condition for long-wave transverse instability is completely determined by these functionals. Whereas longitudinal instability is determined by a single partial derivative (the Vakhitov-Kolokolov criterion), the condition for transverse instability requires 10 partial derivatives. The theory is illustrated by application to scalar NLS equations with general potential, and vector NLS equations for optical media with χ<i><sup>(2)</i></sup> nonlinearity.</p>

Item Type: Article
Additional Information: Published in Proceedings of the Royal Society of London A, 460, 2605-2615. © 2004 The Royal Society. All rights reserved. To visit the official publication site click here
Uncontrolled Keywords: Solitary Waves, Optical Media, Transverse Instability, Multi-Symplectic, Nonlinear Schrödinger Equation, Hamiltonian
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:42
Last Modified: 07 Nov 2013 14:00
URI: http://epubs.surrey.ac.uk/id/eprint/1534

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