The regularized Benjamin–Ono equation appears in the modeling of long-crested interfacial waves in two-fluid systems. For this equation, Fourier–Galerkin and collocation semi-discretizations are proved to be spectrally convergent. A new exact solution is found and used for the experimental validation of the numerical algorithm. The scheme is then used to study the interaction of two solitary wa...

The regularized layered medium equation is proposed as a model of voltage distribution in a medium consisting of alternating thin films of conducting and dielectric materials. This equation is obtained from the layered medium equation by the introduction of a regularizing perturbation that takes account of the resistance at the interface between adjacent conducting and dielectric layers. The re...

In this article, we give the extended trial equation method for solving nonlinear partial differential equations with higher order nonlinearity. By use of this method, the exact travel-ing wave solutions including soliton solution, singular soliton solutions, rational function solution and elliptic integral function solution to one-dimensional general improved KdV (GIKdV) equation and Rðm; nÞ e...

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using Sinc-collocation method. This approach approximates space dimension with cardinal expansion Sinc functions. First, discretizing time derivative MRLW by classic finite difference formula, while derivatives are approximated θ—weighted scheme. For comparison purposes, we also find soliton Ad...

We give a brief survey of applications of the Gearhart-Prüss spectral mapping theorem for abstract strongly continuous semigroups on Hilbert spaces to the study of stability of solitary waves for a large class of Hamiltonian partial differential equations of mathematical physics including Klein-Gordon, nonlinear Schrödinger, Boussinesq, Benjamin-BonaMahoney (regularized long-wave), Korteweg-deV...

Abstract We study integrability properties of the non-chiral intermediate long wave equation recently introduced by authors as a parity-invariant variant equation. For this new we: (a) derive Lax pair, (b) Hirota bilinear form, (c) Bäcklund transformation, (d) use, separately, transformation and representation to obtain an infinite number conservation laws.