On a periodic solution of the focusing nonlinear Schr\"odinger equation
Mathematical Physics
2014-07-31 v1 math.MP
Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1407.7974,
title = {On a periodic solution of the focusing nonlinear Schr\"odinger equation},
author = {A. O. Smirnov and E. G. Semenova and V. Zinger and N. Zinger},
journal= {arXiv preprint arXiv:1407.7974},
year = {2014}
}
Comments
24 pages, 9 figures