Geodesic
Real-analytic solutions of the nonlinear Schr\"odinger equation
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 205-218

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We establish that the Riemann problem on the factorization of formal matrix-valued Laurent series subject to unitary symmetry has a solution. As an application, we show that any local real-analytic solution (in $ x$ and $ t$) of the focusing nonlinear Schrödinger equation has a real-analytic extension to some strip parallel to the $ x$-axis and that in each such strip there exists a solution that cannot be extended further. 
@article{MMO_2014_75_2_a6,
     author = {A. V. Domrin},
     title = {Real-analytic solutions of the nonlinear {Schr\"odinger} equation},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {205--218},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a6/}
}
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A. V. Domrin. Real-analytic solutions of the nonlinear Schr\"odinger equation. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 205-218. http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a6/