Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Lee, Jyh HaoPublisher: search.filters.publisher.IOP Publishing Ltd.

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  • Conference Object
    Citation - WoS: 1
    Resonant Dispersive Benney and Broer-Kaup Systems in 2+1 Dimensions
    (IOP Publishing Ltd., 2014) Lee, Jyh Hao; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We represent the Benney system of dispersionless hydrodynamic equations as NLS type infinite system of equations with quantum potential. We show that negative dispersive deformation of this system is an integrable system including vector generalization of Resonant NLS and 2+1 dimensional nonlocal Resonant NLS. We obtain bilinear form and soliton solutions in these systems and find the resonant character of soliton interaction. Equivalent vector Broer-Kaup system and non-local 2+1 dimensional nonlocal Broer-Kaup equation are constructed.
  • 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.