Browsing Natural and Mathematical Sciences by Author "(ORCID 000000025167609X & YÖK ID 119316) Erbay, Hüsnü Ata"
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The CamassaHolm equation as the longwave limit of the improved Boussinesq equation and of a class of nonlocal wave equations
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (AIMS, 201611)In the present study we prove rigorously that in the longwave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions ... 
Comparison of nonlocal nonlinear wave equations in the longwave limit
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (Taylor & Francis, 20201117)We consider a general class of convolutiontype nonlocal wave equations modeling bidirectional nonlinear wave propagation. The model involves two small positive parameters measuring the relative strengths of the nonlinear ... 
Convergence of a semidiscrete numerical method for a class of nonlocal nonlinear wave equations
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (EDP Sciences, 20180913)In this article, we prove the convergence of a semidiscrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. ... 
Derivation of the CamassaHolm equations for elastic waves
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (Elsevier, 20150605)In this paper we provide a formal derivation of both the Camassa–Holm equation and the fractional Camassa–Holm equation for the propagation of smallbutfinite amplitude long waves in a nonlocally and nonlinearly elastic ... 
Local existence of solutions to the initialvalue problem for onedimensional strainlimiting viscoelasticity
Erbay, Hüsnü Ata; Erkip, A.; Şengül, Y. (Elsevier, 20201115)In this work we prove local existence of strong solutions to the initialvalue problem arising in onedimensional strainlimiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized ... 
Longtime existence of solutions to nonlocal nonlinear bidirectional wave equations
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (American Institute of Mathematical Sciences, 201905)We consider the Cauchy problem defined for a general class of nonlocal wave equations modeling bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution ... 
Numerical computation of solitary wave solutions of the Rosenau equation
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (Elsevier, 202011)We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave ... 
A semidiscrete numerical method for convolutiontype unidirectional wave equations
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (Elsevier, 2019)Numerical approximation of a general class of nonlinear unidirectional wave equations with a convolutiontype nonlocality in space is considered. A semidiscrete numerical method based on both a uniform space discretization ... 
Some remarks on the stability and instability properties of solitary waves for the double dispersion equation
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (Estonian Academy of Sciences, 2015)In this article we give a review of our recent results on the instability and stability properties of travelling wave solutions of the double dispersion equation utt − uxx + auxxxx − buxxtt = −(up−1u)xx for p > 1, a ≥ b ... 
A thermodynamically consistent stressrate type model of onedimensional strainlimiting viscoelasticity
Erbay, Hüsnü Ata; Sengul, Y. (Springer Nature, 20200528)We introduce a onedimensional stressrate type nonlinear viscoelastic model for solids that obey the assumptions of the strainlimiting theory. Unlike the classical viscoelasticity theory, the critical hypothesis in the ... 
Traveling waves in onedimensional nonlinear models of strainlimiting viscoelasticity
Erbay, Hüsnü Ata; Şengül, Yasemin (Elsevier, 201512)In this paper we investigate traveling wave solutions of a nonlinear differential equation describing the behaviour of onedimensional viscoelastic medium with implicit constitutive relations. We focus on a subclass of ... 
Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A. (Estonian Academy of Sciences, 2015)We consider unidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral with a suitable kernel function. We first give a brief review of ...
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