Further extension of the generalized and improved (G0/G)-expansion method; Nonlinear ordinary differential equation; ZKBBM equation; Travelling wave solutions Abstract In this article, the generalized and improved (G0/G)-expansion method has been proposed for further extension to generate many new travelling wave solutions. In addition, nonlinear ordinary differential equation is implemented as...

The cubic complex one-dimensional Ginzburg–Landau equation is considered. Using the Hone’s method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave no elliptic travelling wave solution. This result amplifies the Hone’s result, that this equation has no elliptic travelling wave solution.

We study travelling-wave solutions for a reaction-diffusion system arising as a model for host-tissue degradation by bacteria. This system consists of a parabolic equation coupled with an ordinary differential equation. For large values of the ‘degradation-rate parameter’ solutions are well approximated by solutions of a Stefan-like free boundary problem, for which travelling-wave solutions can...

This paper is concerned with the asymptotic convergence of numerical solutions toward discrete travelling waves for a class of relaxation numerical schemes, approximating the scalar conservation law. It is shown that if the initial perturbations possess some algebraic decay in space, then the numerical solutions converge to the discrete travelling wave at a corresponding algebraic rate in time,...

The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the study of a singular nonlinear integral equation. This article is devoted to demonstrating how this c...

The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions an...

This article addresses orbital stability of periodic travelling-wave solutions for coupled nonlinear Schrödinger equations. We prove the existence of smooth curves of periodic travelling-wave solutions depending on the dnoidal-type functions. Orbital stability analysis is developed in the context of Hamiltonian systems. We consider both the stability problem by periodic perturbations which have...

We consider a simplified model of vertical non-static groundwater flow, resulting in a Burgers’ diffusive equation extended with a third order term with mixed derivatives in space and time. This model is motivated by previous work on the existence of travelling wave solutions on a more general model. We investigate stability of travelling wave solutions of the simplified model, for which we fir...