Wave Propogation in Nonlinear Implicit Lattices

Professor Vassilios Rothos (Aristotle University of Thessaloniki)

  • Wed 5 Dec 18

    14:00 - 16:00

  • Colchester Campus


  • Event speaker

    Professor Vassilios Rothos

  • Event type

    Lectures, talks and seminars
    Department of Mathematical Sciences Seminar

  • Event organiser

    Mathematical Sciences, Department of

  • Contact details

    Dr Andrew Harrison

We study the existence and uniqueness results of periodic and asymptotic travelling waves of nonlinear lattices in implicit form. In particular, we consider damped nonlinear lattices driven by external forces. The dissipative nonlinear lattices describe the magnetic metamaterials have also mechanical analogues. Localized solutions include solitary waves of permanent form and traveling breathers which appear time periodic in a system of reference moving at constant velocity are studied. We obtain a general criterion for spectral stability of multi-site breathers for a small coupling constant. For the metamaterial lattices, we focus on periodic traveling wave due to the presence of periodic force. We employ topological and variational methods to study the existence and the stability of periodic waves The existence and the stability of asymptotic waves are also computed and discussed numerically.

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