On the Complex Stationary Nearly Solitary Waves

  • L. A. Beljakov
  • L. P. Šil’nikov
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 28)


When studying the mathematical models of various strongly nonlinear physical, chemical and other processes, the solutions of travelling stationary wave type are of special interest. The search for such solutions is specific and it is usually reduced to a study of peculiar trajectories, viz. heteroclinic and homoclinic orbits of finite-dimensional self-similar systems which may be investigated by the methods of qualitative theory of dynamical systems. Heteroclinic trajectories going from one equilibrium state to another correspond to travelling waves of the wave-front type which are typical for the Kolmogorov-Petrovsky-Piskunov equation (KPP-equation) as well as for equations of combustion, gas dynamics, and so on. Homoclinic trajectories, running from an equillibrium state and back to it, correspond to travelling waves called impulses or solitons (the Korteweg-de Vries equation, Fritz-Hugh-Nagumo equation, etc.).


Solitary Wave Periodic Motion Homoclinic Orbit Nauk USSR Jordan Cell 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • L. A. Beljakov
    • 1
  • L. P. Šil’nikov
    • 1
  1. 1.Scientific Research Institute for Applied Mathematics and CyberneticsGorky State UniversitySU-GorkyUSSR

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