Narrow Results

This paper implements bifurcation method and the rational sine-Gordon expansion method to investigate the dynamical behavior of traveling wave solutions of a 2D complex Ginzburg–Landau equation. By varying the parameters, we obtained traveling wave solutions including the periodic wave solutions, solitary wave solution, kink and anti-kink wave solution and in addition by using the rational sine-Gordon expansion method, we determined bright and dark soliton which have a great contribution in the long distance telecommunication system.

In this paper, the bifurcation method of dynamical systems is employed to study the Camassa–Holm equation

In this paper, we prove the existence of coexistence states for a nonlocal singular elliptic system that arises from the interaction between amoeba and bacteria populations. Our study is based on fixed point arguments using a version of the Bolzano’s theorem, for which we will first analyze a local system by bifurcation theory. Moreover, we study the behavior of the coexistence region obtained and we interpret our results according to the growth rate of both species.

This paper deals with a nonlocal diffusion elliptic eigenvalue problem. Specifically, the diffusion of the unknown variable at a point of the domain depends on its value in a neighborhood of the point. We apply bifurcation arguments and appropriate approximation to obtain our results. Some applications to the population dynamics will be given.