Asymptotics of an autoresonance soliton

O. M. Kiselev

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 128-136

Résumé

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.

Détail

Keywords: autoresonance; phase locking; soliton.

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