Integrability in Action: Solitons, Instability and Rogue Waves

Antonio Degasperis, Sara Lombardo

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

10 Citations (Scopus)

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.
Original languageEnglish
Title of host publicationRogue and Shock Waves in Nonlinear Dispersive Media
EditorsMiguel Onorato, Stefania Resitori, Fabio Baronio
Place of PublicationLondon
PublisherSpringer
Pages23-53
Volume926
ISBN (Print)978-3-319-39212-7
DOIs
Publication statusE-pub ahead of print - 20 Sep 2016

Publication series

NameLecture Notes in Physics
PublisherSpringer
ISSN (Electronic)0075-8450

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