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Theoretical and Mathematical Physics

, Volume 167, Issue 3, pp 762–771 | Cite as

Asymptotic analysis of a model of nuclear magnetic autoresonance

  • L. A. KalyakinEmail author
  • O. A. Sultanov
  • M. A. Shamsutdinov
Article

Abstract

We study the system of three first-order differential equations arising when averaging the Bloch equations in the theory of nuclear magnetic resonance. For the averaged system, we construct an asymptotic series for the stable solution with an infinitely increasing amplitude. This result gives a key to understanding the autoresonance in weakly dissipative magnetic systems as a phenomenon of significant growth of the magnetization initiated by a small external pumping.

Keywords

nonlinear equation perturbation small parameter asymptotic behavior autoresonance dissipation stability 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • L. A. Kalyakin
    • 1
    Email author
  • O. A. Sultanov
    • 2
  • M. A. Shamsutdinov
  1. 1.Institute of MathematicsRASUfaRussia
  2. 2.Ufa State Aircraft Technical UniversityUfaRussia

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