Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Computation and stability of waves in equivariant evolution equations

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant evolution equa- tion. In numerical computations the freezing method takes advantage of this structure by splitting the evolution of the PDE into the dynamics on the underlying Lie group and on some reduced phase space. The approach raises a series of questions which were answered to a certain degree by the project: linear stability implies non-linear (asymp- totic) stability, persistence of stability under discretisation, analysis and computation of spectral structures, first versus second order evolution systems, well-posedness of partial differential algebraic equations, spatial decay of wave profiles and truncation to bounded domains, analytical and numerical treatment of wave interactions, relation to connecting orbits in dynamical systems. A further numerical problem related to this topic will be discussed, namely the solution of non-linear eigenvalue problems via a contour method.

      Related collections

      Most cited references 28

      • Record: found
      • Abstract: not found
      • Article: not found

      Euclidean symmetry and the dynamics of rotating spiral waves

        Bookmark
        • Record: found
        • Abstract: not found
        • Article: not found

        Stability of Travelling Waves

          Bookmark
          • Record: found
          • Abstract: not found
          • Article: not found

          The Numerical Computation of Connecting Orbits in Dynamical Systems

           W.-J. BEYN (1990)
            Bookmark

            Author and article information

            Journal
            29 October 2018
            1810.12168

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            37Lxx, 65J08, 74J30, 65L15, 35B40
            math.NA

            Numerical & Computational mathematics

            Comments

            Comment on this article