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Dynamics of large-amplitude solitons

  • Nonlinear Physics
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Abstract

The interaction and generation of solitons in nonlinear integrable systems which allow the existence of a soliton of limiting amplitude are considered. The integrable system considered is the Gardner equation, which includes the Korteweg-de Vries equation (for quadratic nonlinearity) and the modified Korteweg-de Vries equation (for cubic nonlinearity) as special cases. A two-soliton solution of the Gardner equation is derived, and a criterion, which distinguishes between different scenarios for the interaction of two solitons, is determined. The evolution of an initial pulsed disturbance is considered. It is shown, in particular, that solitons of opposite polarity appear during such evolution on the crest of a limiting soliton.

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Authors and Affiliations

  1. Nizhnii Novgorod State University, 603600, Nizhnii Novgorod, Russia

    A. V. Slyunyaev

  2. Institute of Applied Physics, Russian Academy of Sciences, 603600, Nizhnii Novgorod, Russia

    E. N. Pelinovski

Authors
  1. A. V. Slyunyaev
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  2. E. N. Pelinovski
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Zh. Éksp. Teor. Fiz. 116, 318–335 (July 1999)

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Slyunyaev, A.V., Pelinovski, E.N. Dynamics of large-amplitude solitons. J. Exp. Theor. Phys. 89, 173–181 (1999). https://doi.org/10.1134/1.558966

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  • DOI: https://doi.org/10.1134/1.558966

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