Problems of Existence of Nontopological Solitons (Breathers) for Nonlinear Klein-Gordon Equations

  • Vladimir Eleonsky
Part of the NATO ASI Series book series (NSSB, volume 284)


The main goal of the present lecture is to present the results obtained by our group on investigations of the soliton-type states for nonlinear wave equations of the form
$$ {u_{{tt}}} - {u_{{xx}}} - g(u) = 0,g(0) = 0,{g_{u}}(0)\angle 0 $$
and to discuss a number of unsolved problems of common interest. In spite of the fact that historically, investigations of these problems were led by analysis of corresponding asymptotic expansions, I think that a quantitative theory of dynamical systems must be the basis for a correct interpretation of asymptotic and numerical-analysis results. In the lecture only references to English-language publications of our group are presented.


Singular Point Hamiltonian System Center Manifold Nonlinear Wave Equation Homoclinic Loop 
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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Vladimir Eleonsky
    • 1
  1. 1.Lukin’s Physical Research InstituteMoscowUSSR

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