An extended mapping method is used to drive some new exact travelling wave solutions of nonlinear evolution equations arising in physics,namely,generalized Hirota-Satsuma coupled KdV system and coupled Maccaris equations.As a result,many exact travelling wave solutions are obtained which include new solitary wave solutions,triangular and hyperbolic functions.Solutions in the limiting cases have...

This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of “desirable pair of upper-lower solutions”, through which a subset can be constructed. We then apply the Schauder’s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.

We consider a model for the propagation of a subsonic detonation wave through a porous medium introduced by Sivashinsky [8]. We show that it admits travelling wave solutions that converge in the limit of zero temperature diffusivity to the travelling fronts of a reduced system constructed in [6].

Simultaneous pulse generation from ground state and excited state transitions in a two-section quantum-dot laser is studied via a finite-difference travelling-wave model; design rules to obtain stable dual-wavelength mode-locking regime over a wide range of bias current and voltage are proposed. Quantum-dot laser; passive mode-locking; two-state lasing; finite-difference travelling-wave model;

We study travelling wave solutions for a class of fourth order parabolic equations. Travelling wave fronts of the form u(x, t) = U(x + ct), connecting homogeneous states, are proven to exist in various cases: connections between two stable states, as well as connections between an unstable and a stable state, are considered.

We investigate the diffusive Leslie–Gower predator–prey model. Travelling wave solutions were found and a minimum wave speed relationship was derived. Linear stability analysis was performed in addition to full numerical simulation of the model. All travelling waves were found to be stable. © 2015 Elsevier Inc. All rights reserved.

A class of particular travelling wave solutions of the generalized Benjamin-BonaMahony equation are studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered. Pacs:05.45.Yv, 52.35.Mw, 52.35.Sb, 02.30.Jr

The Eckhaus stability boundaries of travelling periodic roll patterns arising in binary fluid convection is analysed using high-resolution numerical methods. We present results corresponding to three different values of the separation ratio used in experiments. Our results show that the subcritical branches of travelling waves bifurcating at the onset of convection suffer sideband instabilities...

We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with zero speed of propagation with exactly the same profile as the original one. This procedure allows us to compute simultaneously th...