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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 1, Pages 128–136 (Mi timm1149)  

Asymptotics of an autoresonance soliton

O. M. Kiselev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa

Abstract: Phase locking is studied in a one-dimensional medium under the action of an external force with slowly changing frequency. In a typical situation, the phase locking is described by a nonstationary nonlinear Schrodinger equation with external force. For large values of the time variable, the leading term of a space-localized growing asymptotic solution with soliton profile in the principal order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external perturbation with decreasing magnitude. Necessary growth conditions are deduced for such a solution under dissipation.

Keywords: autoresonance; phase locking; soliton.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, 293, suppl. 1, 75–84

Bibliographic databases:

UDC: 517.977
Received: 10.12.2014

Citation: O. M. Kiselev, “Asymptotics of an autoresonance soliton”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 128–136; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 75–84

Citation in format AMSBIB
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