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Exponentially Small Oscillations in the Solution of an Ordinary Differential Equation

  • Chapter
Asymptotics beyond All Orders

Part of the book series: NATO ASI Series ((NSSB,volume 284))

Abstract

The solutions of the equation

$${\varepsilon ^{2}}{y^{{''}}} = {y^{2}} - {t^{2}} - 1, - \infty < t < \infty $$
((1.1))

are discussed in the limit as ε → 0. This equation arises as a connection problem in the theory of resonant oscillations in a tank1,2.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Edinburgh, The Kings Buildings, Edinburgh, EH9 3JZ, Scotland

    J. G. Byatt-Smith & A. M. Davie

Authors
  1. J. G. Byatt-Smith
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  2. A. M. Davie
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Editor information

Editors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    Harvey Segur

  2. Ohio State University, Columbus, Ohio, USA

    Saleh Tanveer

  3. University of California, San Diego, La Jolla, California, USA

    Herbert Levine

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© 1991 Plenum Press, New York

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Byatt-Smith, J.G., Davie, A.M. (1991). Exponentially Small Oscillations in the Solution of an Ordinary Differential Equation. In: Segur, H., Tanveer, S., Levine, H. (eds) Asymptotics beyond All Orders. NATO ASI Series, vol 284. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0435-8_16

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  • DOI: https://doi.org/10.1007/978-1-4757-0435-8_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0437-2

  • Online ISBN: 978-1-4757-0435-8

  • eBook Packages: Springer Book Archive

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