Behavior of gap solitons in anharmonic lattices

Aurélien Serge Tchakoutio Nguetcho, Guy Merlin Nkeumaleu, and Jean Marie Bilbault
Phys. Rev. E 96, 022207 – Published 14 August 2017

Abstract

Using the theory of bifurcation, we provide and find gap soliton dynamics in a nonlinear Klein-Gordon model with anharmonic, cubic, and quartic interactions immersed in a parametrized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Nonconvex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive a variety of exotic solutions corresponding to the phase trajectories under different parameter conditions. Moreover, we demonstrate how and why traveling waves lose their smoothness and develop into solutions with compact support or breaking.

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  • Received 14 April 2017

DOI:https://doi.org/10.1103/PhysRevE.96.022207

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsInterdisciplinary PhysicsGeneral PhysicsNetworks

Authors & Affiliations

Aurélien Serge Tchakoutio Nguetcho*

  • Département de Physique, Laboratoire Interdisciplinaire des Sciences et Sciences Appliquées du Sahel (LISSAS), Faculté des Sciences, Université de Maroua, Boîte Postale 814, Maroua, Cameroun

Guy Merlin Nkeumaleu and Jean Marie Bilbault

  • Laboratoire LE2I FRE 2005, CNRS, Arts et Métiers, Université de Bourgogne Franche-Comté, Dijon, France

  • *Also at Laboratoire LE2I FRE 2005, CNRS, Arts et Métiers, Université de Bourgogne Franche-Comté, Dijon, France; corresponding author: nguetchoserge@yahoo.fr
  • nkeumaleu@yahoo.fr
  • bilbault@u-bourgogne.fr

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Issue

Vol. 96, Iss. 2 — August 2017

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