Integrability in Action: Solitons, Instability and Rogue Waves

Degasperis, Antonio and Lombardo, Sara (2016) Integrability in Action: Solitons, Instability and Rogue Waves. In: Rogue and Shock Waves in Nonlinear Dispersive Media. Lecture Notes in Physics, 926 . Springer, London, pp. 23-53. ISBN 978-3-319-39212-7

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Official URL: http://dx.doi.org/10.1007/978-3-319-39214-1_2

Abstract

Integrable nonlinear equations modeling wave phenomena play an important role in understanding and predicting experimental observations. Indeed, even if approximate, they can capture important nonlinear effects because they can be derived, as amplitude modulation equations, by multiscale perturbation methods from various kind of wave equations, not necessarily integrable, under the assumption of weak dispersion and nonlinearity. Thanks to the mathematical property of being integrable, a number of powerful computational techniques is available to analytically construct special interesting solutions, describing coherent structures such as solitons and rogue waves, or to investigate patterns as those due to shock waves or behaviors caused by instability. This chapter illustrates a selection of these techniques, using first the ubiquitous Nonlinear Schrödinger (NLS) equation as a prototype integrable model, and moving then to the Vector Nonlinear Schrödinger (VNLS) equation as a natural extension to wave coupling.

Item Type: Book Section
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Related URLs:
Depositing User: Becky Skoyles
Date Deposited: 06 Oct 2016 10:12
Last Modified: 04 Apr 2017 13:56
URI: http://nrl.northumbria.ac.uk/id/eprint/27937

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