Soliton ensembles and solitonic structures

Abstract

The article deals with the analysis of three complicated one-dimensional evolution equations, the solutions of which can be classified as soliton ensembles or solitonic structures. The case studies from the physical viewpoint are: (i) martensitic–austenitic alloys; (ii) hyperelastic rod and (iii) granular materials. The corresponding evolution equations governing the propagation of longitudinal waves include higher order nonlinear and dispersive terms and are nonintegrable. Numerical simulation is carried out by the pseudospectral method. The first class of solutions involves solitons with nonvanishing oscillatory tails and wave packets called solitonic structures. The second class includes special soliton ensembles or more exactly – plaited solitons. The emergence of such entities and their interaction demonstrate the solitonic character of waves.

Keywords:

• dispersion
• nonlinearities
• evolution equations
• solitonic structures
• soliton ensembles

AMS Subject Classifications::

• 35Q74
• 74J30
• 74J35
• 65M70

Acknowledgement

The support from the Estonian Science Foundation (Grant No. 8658) and the Ministry of Education and Research (SF0140077s08) is gratefully acknowledged.