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Periodic solutions of the Hopf equation

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Abstract

We consider the long-time dynamics of approximate solutions of the boundary-value problem for the Hopf equation on a finite segment. Together with the initial conditions, for instance, we impose the zero Dirichlet conditions on both ends of the segment. In this case, all features of solutions associated with the intersections of characteristics are accumulated on a strip bounded by the vertical characteristics emitted from the boundary points.

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Authors and Affiliations

  1. Aliev Karachaev-Cherkess State University, Karachaevsk, Russia

    A. B. Shabat

  2. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

    A. B. Shabat

Authors
  1. A. B. Shabat
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Correspondence to A. B. Shabat.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 175, No. 1, pp. 222–230, November, 2013.

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Shabat, A.B. Periodic solutions of the Hopf equation. Theor Math Phys 177, 1471–1478 (2013). https://doi.org/10.1007/s11232-013-0116-z

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  • DOI: https://doi.org/10.1007/s11232-013-0116-z

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