Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c 0 ∗ > such that for each c c∗ ≥ , the systems under consideration admit monotonic nondecreasing traveling waves.

In this paper, we established traveling wave solutions of the nonlinear evolution equation. The sine-cosine method was used to construct travelling wave solutions of the Fitzhugh-Nagumo equation and Cahn-Allen equation. Graphical interpretation shows that obtained results include periodic and Soliton wave solutions. It is also shown that for α =−1, solutions of Fitzhugh-Nagumo equation coincide...

For the Allen-Cahn equation, it is well known that there a monotone standing wave joining with balanced wells of potential. In this paper we study existence traveling solutions for equation on an infinite channel. Such possess large number oscillation and they are obtained aid variational arguments.

The hyperbolic tangent (tanh) method is a powerful technique to symbolically compute traveling waves solutions of one-dimensional nonlinear wave and evolution equations. In particular, the method is well suited for problems where dispersion, convection, and reactiondiffusion phenomena play an important role. The technique is outlined for the computation of closedform tanh-solutions for nonlinea...

A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3 + 1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is...