Diego Alonso-Orán , Angel Durán , Rafael Granero-Belinchón
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On the existence of traveling wave solutions for cold plasmas
The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field. First, using bifurcation theory, we can rigorously prove the existence of periodic traveling waves of small amplitude. Furthermore, our analysis also evidences the existence of different type of traveling waves. To this end, we present a second approach based on the analysis of the differential system satisfied by the traveling wave profiles, the existence of equilibria, and the identification of associated homoclinic and periodic orbits around them. The study makes use of linearization techniques, normal forms, and numerical computations to show the existence of different types of traveling wave solutions, with monotone and non-monotone behavior and different regularity, as well as periodic traveling waves.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.