Zobrazeno 1 - 10
of 222
pro vyhledávání: '"ERBAY, S"'
Publikováno v:
Applicable Analysis, 102, 4422-4431 (2022)
In this work, we prove a comparison result for a general class of nonlinear dispersive unidirectional wave equations. The dispersive nature of one-dimensional waves occurs because of a convolution integral in space. For two specific choices of the ke
Externí odkaz:
http://arxiv.org/abs/2209.07904
Publikováno v:
Wave Motion 114 (2022) 103015
Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev-Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies analogous full dispersive KP
Externí odkaz:
http://arxiv.org/abs/2208.06017
Publikováno v:
Applied Numerical Mathematics 175, 29-39 (2022)
A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidirectional wave equations previously studied by the addition of a linear
Externí odkaz:
http://arxiv.org/abs/2202.01262
Publikováno v:
Physica D: Nonlinear Phenomena 427, Article number: 133010 (2021)
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation of nonlinear waves in a continuous medium. In the limit of vanishing nonlocality we study the behavior of solutions to the Cauchy problem. We p
Externí odkaz:
http://arxiv.org/abs/2107.09108
Publikováno v:
Wave Motion 98, Article number: 102618 (2020)
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 solutions. We then apply two n
Externí odkaz:
http://arxiv.org/abs/2008.00278
Publikováno v:
Journal of Computational and Applied Mathematics 387, Article Number: 112496 (2021)
Numerical approximation of a general class of nonlinear unidirectional wave equations with a convolution-type nonlocality in space is considered. A semi-discrete numerical method based on both a uniform space discretization and the discrete convoluti
Externí odkaz:
http://arxiv.org/abs/1909.10917
Publikováno v:
Applicable Analysis 99, 2668-2677 (2020)
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional nonlinear wave propagation. The model involves two small positive parameters measuring the relative strengths of the nonlinear and dispersive effects. We t
Externí odkaz:
http://arxiv.org/abs/1901.01461
Publikováno v:
Discrete and Continuous Dynamical Systems 39, 2877-2891 (2019)
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 integral. We prove a lo
Externí odkaz:
http://arxiv.org/abs/1807.02822
Publikováno v:
ESAIM: Mathematical Modelling and Numerical Analysis 52, 803-826 (2018)
In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. The most important characteri
Externí odkaz:
http://arxiv.org/abs/1805.07264
Publikováno v:
Discrete and Continuous Dynamical Systems 37, 3111-3122 (2017)
We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equa
Externí odkaz:
http://arxiv.org/abs/1701.03491