The European Physical Journal Special Topics

, Volume 225, Issue 6–7, pp 943–958 | Cite as

Nonlinear wave propagation in discrete and continuous systems

Review Session A: Reviews
Part of the following topical collections:
  1. Mathematical Modeling of Complex Systems

Abstract

In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.

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Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Laboratory of Nonlinear Mathematicsand Aristotle University of ThessalonikiThessalonikiGreece

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