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Yazar: Erbay, Saadet × WoS Q: Q2 ×

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Listeleniyor 1 - 6 / 6
  • Küçük Resim
    Yayın
    Standing waves for a generalized Davey-Stewartson system
    (IOP Publishing, 2006-10-27) Eden, Osman Alp; Erbay, Saadet
    In this paper, we establish the existence of non-trivial solutions for a semi-linear elliptic partial differential equation with a non-local term. This result allows us to prove the existence of standing wave ( ground state) solutions for a generalized Davey-Stewartson system. A sharp upper bound is also obtained on the size of the initial values for which solutions exist globally.
  • Küçük Resim
    Yayın
    The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
    (IOP Publishing Ltd, 2011-04) Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, Albert
    This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in L-2 Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.
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    Coupled quintic nonlinear Schrodinger equations in a generalized elastic solid
    (IOP Publishing Ltd, 2004-10-08) Hacınlıyan, Irma; Erbay, Saadet
    In the present study, the nonlinear modulation of transverse waves propagating in a cubically nonlinear dispersive elastic medium is studied using a multiscale expansion of wave solutions. It is found that the propagation of quasimonochromatic transverse waves is described by a pair of coupled nonlinear Schrodinger (CNLS) equations. In the process of deriving the amplitude equations, it is observed that for a specific choice of material constants and wavenumber, the coefficient of nonlinear terms becomes zero, and the CNLS equations are no longer valid for describing the behaviour of transverse waves. In order to balance the nonlinear effects with the dispersive effects, by intensifying the nonlinearity, a new perturbation expansion is used near the critical wavenumber. It is found that the long time behaviour of the transverse waves about the critical wavenumber is given by a pair of coupled quintic nonlinear Schrodinger (CQNLS) equations. In the absence of one of the transverse waves, the CQNLS equations reduce to the single quintic nonlinear Schrodinger (QNLS) equation which has already been obtained in the context of water waves. By using a modified form of the so-called tanh method, some travelling wave solutions of the CQNLS equations are 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.
  • Küçük Resim
    Yayın
    Global existence and nonexistence results for a generalized Davey-Stewartson system
    (IOP Publishing, 2004-12-03) Babaoğlu, Ceni; Eden, Osman Alp; Erbay, Saadet
    We consider a system of three equations, which will be called generalized Davey-Stewartson equations, involving three coupled equations, two for the long waves and one for the short wave propagating in an infinite elastic medium. We classify the system according to the signs of the parameters. Conserved quantities related to mass, momentum and energy are derived as well as a specific instance of the so-called virial theorem. Using these conservation laws and the virial theorem both global existence and nonexistence results are established under different constraints on the parameters in the elliptic-elliptic-elliptic case.
  • Küçük Resim
    Yayın
    Stability of solitary waves for three-coupled long wave-short wave interaction equations
    (Oxford Univ Press, 2011-08) Borluk, Handan; Erbay, Saadet
    In this paper, we consider a three-component system of 1D long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions using variational methods.