Geodesic
Asymptotics of an autoresonance soliton
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 128-136

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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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     author = {O. M. Kiselev},
     title = {Asymptotics of an autoresonance soliton},
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     pages = {128--136},
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     volume = {21},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a12/}
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O. M. Kiselev. Asymptotics of an autoresonance soliton. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 128-136. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a12/