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We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type(More)
In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: u tt − Lu xx = B(±|u| p−1 u) xx , p > 1. The main characteristic of this class of equations is the existence of two sources of dispersion, characterized by two coercive pseudo-differential operators L and B.(More)
Assuming the arterial wall is homogeneous, incompressible, isotropic and elastic, a stress-strain relation has been presented for a rat's abdominal aorta. As an illustrating example, the problem of simultaneous inflation and the axial stretch of a cylindrical artery under physiological loading has been solved and then the material coefficients are(More)
The generalized nonlinear Schrödinger (GNLS) equation is solved numerically by a split-step Fourier method. The first, second and fourth-order versions of the method are presented. A classical problem concerning the motion of a single solitary wave is used to compare the first, second and fourth-order schemes in terms of the accuracy and the computational(More)
  • Hüsnü Ata Erbaya, Saadet Erbaya, Albert Erkipb, H. A. Erbay
  • 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 asymptotic wave models describing the unidirectional propagation of small-but-finite amplitude long waves. When the kernel function is the(More)