Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Whitham–Broer–Kaup Systems in Multi-Dimensions: Quantum and Resonant NLS Connections(World Scientific Publ Co Pte Ltd, 2025) Pashaev, Oktay K.; Rogers, ColinAn overview is presented of quantum and resonant nonlinear Schro<spacing diaeresis>dinger equation links to Whitham-Broer-Kaup type systems. A novel n + 1 dimensional extension of the Whitham-Broer-Kaup hydrodynamic system is constructed with connection to an equivalent multi-dimensional resonant NLS equation. Hybrid Ermakov-Painleve II and associated Painleve XXXIV integrable similarity reductions are derived.Article Citation - WoS: 81Citation - Scopus: 79The Resonant Nonlinear Schrödinger Equation in Cold Plasma Physics. Application of Bäcklund-Darboux Transformations and Superposition Principles(Cambridge University Press, 2007) Lee, Jiunhung; Pashaev, Oktay; Rogers, Colin; Schief, W. K.A system of nonlinear equations governing the transmission of uni-axial waves in a cold collisionless plasma subject to a transverse magnetic field is reduced to the recently proposed resonant nonlinear Schrödinger (RNLS) equation. This integrable variant of the standard nonlinear Schrödinger equation admits novel nonlinear superposition principles associated with Bäcklund-Darboux transformations. These are used here, in particular, to construct analytic descriptions of the interaction of solitonic magnetoacoustic waves propagating through the plasma.Article Citation - WoS: 13Citation - Scopus: 14On a 2+1-Dimensional Whitham-Broer System: a Resonant Nls Connection(John Wiley and Sons Inc., 2011) Rogers, Colin; Pashaev, OktayIt 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: 29Citation - Scopus: 41Soliton resonances in a generalized nonlinear Schrödinger equation(IOP Publishing Ltd., 2008) Pashaev, Oktay; Lee, Jyh Hao; Rogers, ColinIt 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.