Yazar "Borluk, Handan" seçeneğine göre listele

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    Non-existence and existence of localized solitary waves for the two-dimensional long-wave-short-wave interaction equations
    (Elsevier Ltd, 2010-04) Borluk, Handan; Erbay, Hüsnü Ata; Erbay, Saadet
    In this study, we establish the non-existence and existence results for the localized solitary waves of the two-dimensional long-wave-short-wave interaction equations. Both the non-existence and existence results are based on Pohozaev-type identities. We prove the existence of solitary waves by showing that the solitary waves are the minimizers of an associated variational problem.
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    A numerical study of the long wave-short wave interaction equations
    (Elsevier B.V., 2007-03-07) Borluk, Handan; Muslu, Gülçin Mihriye; Erbay, Hüsnü Ata
    Two numerical methods are presented for the periodic initial-value problem of the long wave-short wave interaction equations describing the interaction between one long longitudinal wave and two short transverse waves propagating in a generalized elastic medium. The first one is the relaxation method, which is implicit with second-order accuracy in both space and time. The second one is the split-step Fourier method, which is of spectral-order accuracy in space. We consider the first-, second- and fourth-order versions of the split-step method, which are first-, second- and fourth-order accurate in time, respectively. The present split-step method profits from the existence of a simple analytical solution for the nonlinear subproblem. We numerically test both the relaxation method and the split-step schemes for a problem concerning the motion of a single solitary wave. We compare the accuracies of the split-step schemes with that of the relaxation method. Assessments of the efficiency of the schemes show that the fourth-order split-step Fourier scheme is the most efficient among the numerical schemes considered.
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    Particle dynamics in the KdV approximation
    (Elsevier Science BV, 2012-12) Borluk, Handan; Kalisch, Henrik
    The KdV equation arises in the framework of the Boussinesq scaling as a model equation for waves at the surface of an inviscid fluid. Encoded in the KdV model are relations that may be used to reconstruct the velocity field in the fluid below a given surface wave. In this paper, velocity fields associated to exact solutions of the KdV equation are found, and particle trajectories are computed numerically. The solutions treated here comprise the solitary wave, periodic traveling waves, and the two-soliton solutions. For solitary waves and periodic traveling waves, approximate particle paths are found in closed form.
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    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.