Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Author: search.filters.author.Rogers, ColinSubject: search.filters.subject.Schrödinger equation

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  • Article
    Citation - WoS: 13
    Citation - Scopus: 14
    On a 2+1-Dimensional Whitham-Broer System: a Resonant Nls Connection
    (John Wiley and Sons Inc., 2011) Rogers, Colin; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    It is established that the Whitham-Broer-Kaup shallow water system and the "resonant" nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1-dimensional version of the Whitham-Broer-Kaup system is constructed which, in turn, is equivalent to a recently introduced resonant Davey-Stewartson I system incorporating a Madelung-Bohm type quantum potential. A bilinear representation is adopted and resonant solitonic interaction in this new 2+1-dimensional Kaup-Broer system is exhibited.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 41
    Soliton resonances in a generalized nonlinear Schrödinger equation
    (IOP Publishing Ltd., 2008) Pashaev, Oktay; Pashaev, Oktay; Rogers, Colin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    It is shown that a generalized nonlinear Schrödinger equation proposed by Malomed and Stenflo admits, for a specific range of parameters, resonant soliton interaction. The equation is transformed to the 'resonant' nonlinear Schrödinger equation, as originally introduced to describe black holes in a Madelung fluid and recently derived in the context of uniaxial wave propagation in a cold collisionless plasma. A Hirota bilinear representation is obtained and soliton solutions are thereby derived. The one-soliton solution interpretation in terms of a black hole in two-dimensional spacetime is given. For the two-soliton solution, resonant interactions of several kinds are found. The addition of a quantum potential term is considered and the reduction is obtained to the resonant NLS equation. © 2008 IOP Publishing Ltd.