On solitons in microstructured solids and granular materials

  • Authors:

  • A. Salupere;J. Engelbrecht;O. Ilison;L. Ilison

  • Affiliations:

  • Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Tallinn, Estonia and Department of Mechanics, Tallinn University of Technology, Tallinn, Estonia;Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Tallinn, Estonia;Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Tallinn, Estonia and Department of Mechanics, Tallinn University of Technology, Tallinn, Estonia;Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Tallinn, Estonia and Department of Mechanics, Tallinn University of Technology, Tallinn, Estonia

  • Venue:
  • Mathematics and Computers in Simulation - Special issue: Nonlinear waves: computation and theory IV
  • Year:
  • 2005

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Abstract

The problems under consideration are related to wave propagation in nonlinear dispersive media, characterised by higher-order nonlinear and higher-order dispersive effects. Particularly two problems -- wave propagation in dilatant granular materials and wave propagation in shape-memory alloys -- are studied. Model equations are KdV-like evolution equations in both cases. The types of solutions are determined and analysed. It has been found that waves in granular materials are composed by two concurrent ensembles of solitary waves and there exist a threshold parameter value governing the behaviour of stable waves in alloy type materials.