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2002 - 20094
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Ayarlar

Yazar: Erbay, Saadet × Konu: Nonlinear equations ×

Arama Sonuçları

Listeleniyor 1 - 4 / 4
  • Küçük Resim
    Yayın
    On travelling wave solutions of a generalized Davey-Stewartson system
    (Oxford Univ Press, 2005-02) Eden, Osman Alp; Erbay, Saadet
    The generalized Davey-Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941-949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an infinite elastic medium. The physical parameters (gamma, m(1), m(2), lambda and n) of the system allow one to classify the equations as elliptic-elliptic-elliptic (EEE), elliptic-elliptic-hyperbolic (EEH), elliptic-hyperbolic-hyperbolic (EHH), hyperbolic-elliptic-elliptic (HEE), hyperbolic-hyperbolic-hyperbolic (HHH) and hyperbolic-elliptic-hyperbolic (HEH) (Babaoglu et al., 2004, preprint). In this note, we only consider the EEE and HEE cases and seek travelling wave solutions to GDS systems. By deriving Pohozaev-type identities we establish some necessary conditions on the parameters for the existence of travelling waves, when solutions satisfy some integrability conditions. Using the explicit solutions given in Babaoglu & Erbay (2004) we also show that the parameter constraints must be weaker in the absence of such integrability conditions.
  • 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
    A higher-order model for transverse waves in a generalized elastic solid
    (Pergamon-Elsevier Science, 2002-11) Hacınlıyan, Avadis Simon; Erbay, Saadet
    In the present study, the nonlinear modulation of transverse waves propagating in a generalized elastic solid is studied using a multi-scale expansion of quasi-monochromatic wave solutions. In particular, to include the higher-order nonlinear and dispersive effects in the evolution equations, higher-order perturbation equations are considered, and it is shown that the modulation of two transverse waves is governed by a pair of the coupled higher-order nonlinear Schrodinger (HONLS) equations. In the absence of one of the transverse waves, the coupled HONLS equations reduce to the single HONLS equation that has already been obtained in the context of nonlinear optics. Some special solutions to the coupled HONLS equations are also presented.
  • Küçük Resim
    Yayın
    Two-dimensional wave packets in an elastic solid with couple stresses
    (Pergamon-Elsevier Science Ltd, 2004-08) Babaoğlu, Ceni; Erbay, Saadet
    The problem of (2+1) (two spatial and one temporal) dimensional wave propagation in a bulk medium composed of an elastic material with couple stresses is considered. The aim is to derive (2+1) non-linear model equations for the description of elastic waves in the far field. Using a multi-scale expansion of quasi-monochromatic wave solutions, it is shown that the modulation of waves is governed by a system of three non-linear evolution equations. These equations involve amplitudes of a short transverse wave, a long transverse wave and a long longitudinal wave, and will be called the "generalized Davey Stewartson equations". Under some restrictions on parameter values, the generalized Davey-Stewartson equations reduce to the Davey-Stewartson and to the non-linear Schrodinger equations. Finally, some special solutions involving sech-tanh-tanh and tanh-tanh-tanh type solitary wave solutions are presented.