In this paper, we explore more applications of the hyperbolic function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations (PDES), to special discrete nonlinear equations. Some exact travelling wave solution of the discrete sine-Gordon equation are obtained in terms of hyperbolic fun...

1. Introduction. In this paper we are interested in travelling wave solutions u = u(x; t) of the

In this work, we study the Benjamin-Bona-Mahony like equations with a fully nonlinear dispersive term by means of the factorization technique. In this way we find the travelling wave solutions of this equation in terms of the Weierstrass function and its degenerated trigonometric and hyperbolic forms. Then, we obtain the pattern of periodic, solitary, compacton and kink-like solutions. We give ...

In this paper,an extended mapping method with symbolic computation is developed to obtain new periodic wave solutions in terms of Jacobin elliptic function for nonlinear evolution equations arising in mathematical physics.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 hav...

In this note we analyze a spatially structured SI epidemic model with vertical transmission, a logistic effect on vital dynamics and a density dependent incidence. The dynamics of the underlying system of ordinary differential equations are first shown to exhibit an infinite number of heteroclinic orbits connecting the trivial equilibrium with an interior equilibrium. Our mathematical study of ...

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these me...

The existence of travelling wave solutions for a density-dependent selection migration model in population genetics is proven. A single locus and two alleles are assumed. It is also assumed that the fitnesses of the heterozygotes in the population are below those of the homozygotes. The method of proof is by constructing an isolating neighborhood and computing a connection index. Key words, pop...

Periodic travelling waves (wavetrains) are an important solution type for many partial differential equations. In this paper I review the use of numerical continuation for studying these solutions. I discuss the calculation of the form and stability of a given periodic travelling wave, and the calculation of boundaries in a two-dimensional parameter plane for wave existence and stability. I als...