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The asymptotic behavior of solutions of the sine-gordon equation with singularities at zero

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Abstract

The problem of asymptotic analysis of radially symmetric solutions of the sine-Gordon equation reducible to the third Painlevé transcendent is posed. Solutions with singularities at the origin are studied. For finite values of the independent variable, an asymptotic expansion of such a solution is obtained; the leading term of this expansion is a modulated elliptic function. The corresponding modulation equation and phase shift are written out.

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Authors and Affiliations

  1. Computer Center, Siberian Division of the Russian Academy of Sciences, USSR

    V. L. Vereshchagin

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  1. V. L. Vereshchagin
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Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 329–342, March, 2000.

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Vereshchagin, V.L. The asymptotic behavior of solutions of the sine-gordon equation with singularities at zero. Math Notes 67, 274–285 (2000). https://doi.org/10.1007/BF02676663

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  • DOI: https://doi.org/10.1007/BF02676663

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