On the construction of the exact analytic or parametric closed-form solutions of standing waves concerning the cubic nonlinear Schrödinger equation

We propose a new approach for the construction of the closed-form solutions of standing waves of the cubic nonlinear Schrödinger equation (NLS). Through appropriate functional transformations, we reduce the radially symmetric NLS into an Emden–Fowler equation whose solution results to the derivation...

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Veröffentlicht in:Archive of applied mechanics (1991) 2012-10, Vol.82 (10-11), p.1557-1568
Hauptverfasser: Panayotounakos, D. E., Zarmpoutis, T. I., Siettos, C. I.
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Sprache:eng
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Zusammenfassung:We propose a new approach for the construction of the closed-form solutions of standing waves of the cubic nonlinear Schrödinger equation (NLS). Through appropriate functional transformations, we reduce the radially symmetric NLS into an Emden–Fowler equation whose solution results to the derivation of the closed forms of the standing waves. We also derive the necessary restrictions under which the derived solutions are admissible.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-012-0658-9