Asymptotics of an autoresonance soliton

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• 作者：O. M. Kiselev
• 刊名：Proceedings of the Steklov Institute of Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：293
• 期：1-supp
• 页码：75-84
• 全文大小：278 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8605
• 卷排序：293

文摘

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.Keywordsautoresonancephase lockingsoliton