Asymptotics of an autoresonance soliton
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 Schr¨odinger equation with external force. For large values of the time variable, th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kiselev, O. M. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Proceedings of the Steklov Institute of Mathematics - Berlin : Springer Science+Business Media LLC, 2006, 293(2016), Suppl 1 vom: Juli, Seite 75-84 |
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| Übergeordnetes Werk: |
volume:293 ; year:2016 ; number:Suppl 1 ; month:07 ; pages:75-84 |
| Links: |
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| DOI / URN: |
10.1134/S0081543816050084 |
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| Katalog-ID: |
SPR020276524 |
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| 520 | |a 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 Schr¨odinger 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 main order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external excitation with decreasing amplitude. Necessary growth conditions are deduced for such a solution in the presence of dissipation. | ||
| 650 | 4 | |a autoresonance |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a phase locking |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a soliton |7 (dpeaa)DE-He213 | |
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10.1134/S0081543816050084 doi (DE-627)SPR020276524 (SPR)S0081543816050084-e DE-627 ger DE-627 rakwb eng Kiselev, O. M. verfasserin aut Asymptotics of an autoresonance soliton 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2016 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 Schr¨odinger 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 main order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external excitation with decreasing amplitude. Necessary growth conditions are deduced for such a solution in the presence of dissipation. autoresonance (dpeaa)DE-He213 phase locking (dpeaa)DE-He213 soliton (dpeaa)DE-He213 Enthalten in Proceedings of the Steklov Institute of Mathematics Berlin : Springer Science+Business Media LLC, 2006 293(2016), Suppl 1 vom: Juli, Seite 75-84 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:293 year:2016 number:Suppl 1 month:07 pages:75-84 https://dx.doi.org/10.1134/S0081543816050084 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 293 2016 Suppl 1 07 75-84 |
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10.1134/S0081543816050084 doi (DE-627)SPR020276524 (SPR)S0081543816050084-e DE-627 ger DE-627 rakwb eng Kiselev, O. M. verfasserin aut Asymptotics of an autoresonance soliton 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2016 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 Schr¨odinger 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 main order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external excitation with decreasing amplitude. Necessary growth conditions are deduced for such a solution in the presence of dissipation. autoresonance (dpeaa)DE-He213 phase locking (dpeaa)DE-He213 soliton (dpeaa)DE-He213 Enthalten in Proceedings of the Steklov Institute of Mathematics Berlin : Springer Science+Business Media LLC, 2006 293(2016), Suppl 1 vom: Juli, Seite 75-84 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:293 year:2016 number:Suppl 1 month:07 pages:75-84 https://dx.doi.org/10.1134/S0081543816050084 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 293 2016 Suppl 1 07 75-84 |
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10.1134/S0081543816050084 doi (DE-627)SPR020276524 (SPR)S0081543816050084-e DE-627 ger DE-627 rakwb eng Kiselev, O. M. verfasserin aut Asymptotics of an autoresonance soliton 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2016 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 Schr¨odinger 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 main order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external excitation with decreasing amplitude. Necessary growth conditions are deduced for such a solution in the presence of dissipation. autoresonance (dpeaa)DE-He213 phase locking (dpeaa)DE-He213 soliton (dpeaa)DE-He213 Enthalten in Proceedings of the Steklov Institute of Mathematics Berlin : Springer Science+Business Media LLC, 2006 293(2016), Suppl 1 vom: Juli, Seite 75-84 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:293 year:2016 number:Suppl 1 month:07 pages:75-84 https://dx.doi.org/10.1134/S0081543816050084 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 293 2016 Suppl 1 07 75-84 |
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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 Schr¨odinger 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 main order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external excitation with decreasing amplitude. Necessary growth conditions are deduced for such a solution in the presence of dissipation. © Pleiades Publishing, Ltd. 2016 |
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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 Schr¨odinger 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 main order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external excitation with decreasing amplitude. Necessary growth conditions are deduced for such a solution in the presence of dissipation. © Pleiades Publishing, Ltd. 2016 |
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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 Schr¨odinger 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 main order is constructed. It turned out that a time-growing asymptotic solution can be obtained for an external excitation with decreasing amplitude. Necessary growth conditions are deduced for such a solution in the presence of dissipation. © Pleiades Publishing, Ltd. 2016 |
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