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On the Complex Stationary Nearly Solitary Waves

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Self-Organization Autowaves and Structures Far from Equilibrium

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 28))

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Abstract

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.).

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Author information

Authors and Affiliations

  1. Scientific Research Institute for Applied Mathematics and Cybernetics, Gorky State University, SU-Gorky, USSR

    L. A. Beljakov & L. P. Šil’nikov

Authors
  1. L. A. Beljakov
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  2. L. P. Šil’nikov
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Editor information

Editors and Affiliations

  1. Institute of Biological Physics, USSR Academy of Sciences, SU-142292, Pushchino, USSR

    V. I. Krinsky

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© 1984 Springer-Verlag Berlin Heidelberg

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Beljakov, L.A., Šil’nikov, L.P. (1984). On the Complex Stationary Nearly Solitary Waves. In: Krinsky, V.I. (eds) Self-Organization Autowaves and Structures Far from Equilibrium. Springer Series in Synergetics, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70210-5_19

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  • DOI: https://doi.org/10.1007/978-3-642-70210-5_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-70212-9

  • Online ISBN: 978-3-642-70210-5

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