$On a periodic solution of the focusing nonlinear Schr\"odinger equation$

On a periodic solution of the focusing nonlinear Schr\"odinger equation

A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is investigated. An existence of a real smooth finite-gap solution of...

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Hauptverfasser:	Smirnov, A. O, Semenova, E. G, Zinger, V, Zinger, N
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Mathematical Physics Physics - Exactly Solvable and Integrable Systems Physics - Mathematical Physics Physics - Pattern Formation and Solitons
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Zusammenfassung:	A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is investigated. An existence of a real smooth finite-gap solution of NLS equation with complex initial phase is proven. Degenerations of the constructed solution to one-phase traveling wave solution and solutions in the form of the plane waves are carried.
DOI:	10.48550/arxiv.1407.7974