naa a22 4500 510812503 CHVBK 20180411083449.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1134/S0081543813050064 doi (NATIONALLICENCE)springer-10.1134/S0081543813050064 Garifullin R. Institute of Mathematics with Computing Center, Ufa Research Center of the Russian Academy of Sciences, ul. Chernyshevskogo 112, 450008, Ufa, Russia aut Autoresonance excitation of a soliton of the nonlinear Schrödinger equation [Elektronische Daten] [R. Garifullin] The action of an external parametric perturbation with slowly changing frequency on a soliton of the nonlinear Schrödinger equation is studied. Equations for the time evolution of the parameters of the perturbed soliton are derived. Conditions for the soliton phase locking are found, which relate the rate of change of the perturbation frequency, its amplitude, the wave number, and the phase to the initial data of the soliton. The cases when the initial amplitude of the soliton is small and when the amplitude of the soliton is of the order of unity are considered. Pleiades Publishing, Ltd., 2013 autoresonance nationallicence perturbation nationallicence nonlinear Schrödinger equation nationallicence soliton nationallicence Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 59-63 0081-5438 281<59 2013 281 11501 https://doi.org/10.1134/S0081543813050064 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813050064 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Garifullin R. Institute of Mathematics with Computing Center, Ufa Research Center of the Russian Academy of Sciences, ul. Chernyshevskogo 112, 450008, Ufa, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 59-63 0081-5438 281<59 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer