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On a method for constructing one-frequency solutions of a nonlinear wave equation

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Abstract

A method for constructing one-frequency solutions of nonlinear wave equations is suggested. This approach is based on a modified representation of asymptotic expansions by using special periodic Atebfunctions. This method makes it possible to obtain approximate solution of the problem under consideration without difficulty.

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References

  1. Yu. A. Mitropol'skii and B. I. Moseenkov,Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kiev (1976).

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  2. B. I. Sokil and A. F. Barvins'kyi, “On the asymptotic solution of a nonlinear boundary-value problem,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 1, 22–26 (1980).

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  3. P. M. Senik, “Inversion of an incomplete beta-function,”Ukr. Mat. Zh. 21 No. 3, 325–333 (1969).

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Authors
  1. B. I. Sokil
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Additional information

L'viv Polytechnic Institute, L'viv. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 782–784, June 1994.

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Sokil, B.I. On a method for constructing one-frequency solutions of a nonlinear wave equation. Ukr Math J 46, 853–856 (1994). https://doi.org/10.1007/BF02658188

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  • DOI: https://doi.org/10.1007/BF02658188

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