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Bölüm: Işık Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü × Konu: Dinger equation ×

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  • Küçük Resim
    Yayın
    A note on the amplitude modulation of symmetric regularized long-wave equation with quartic nonlinearity
    (Springer, 2012-12) Demiray, Hilmi
    We study the amplitude modulation of a symmetric regularized long-wave equation with quartic nonlinearity through the use of the reductive perturbation method by introducing a new set of slow variables. The nonlinear Schrodinger (NLS) equation with seventh order nonlinearity is obtained as the evolution equation for the lowest order term in the perturbation expansion. It is also shown that the NLS equation with seventh order nonlinearity assumes an envelope type of solitary wave solution.
  • Küçük Resim
    Yayın
    Reducing a generalized Davey-Stewartson system to a non-local nonlinear Schrodinger equation
    (Pergamon-Elsevier Science Ltd, 2009-07-30) Eden, Osman Alp; Erbay, Saadet; Hacınlıyan, Irma
    In the present study, we consider a generalized (2 + 1) Davey-Stewartson (GDS) system consisting of a nonlinear Schrodinger (NLS) type equation for the complex amplitude of a short wave and two asymmetrically coupled linear wave equations for long waves propagating in an infinite elastic medium. We obtain integral representation of solutions to the coupled linear wave equations and reduce the GDS system to a NLS equation with non-local terms. Finally, we present localized solutions to the GDS system, decaying in both spatial coordinates, for a special choice of parameters by using the integral representation of solutions to the coupled linear wave equations.
  • Küçük Resim
    Yayın
    Closing the gap in the purely elliptic generalized Davey-Stewartson system
    (Pergamon-Elsevier Science Ltd, 2008-10-15) Eden, Osman Alp; Erbay, Hüsnü Ata; Muslu, Gülçin Mihriye
    In this note we improve the results presented previously on global existence and global nonexistence for the Solutions of the purely elliptic generalized Davey-Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.