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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. V. Domrin
TI  - Real-analytic solutions of the nonlinear Schr\"odinger equation
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2014
SP  - 205
EP  - 218
VL  - 75
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a6/
LA  - ru
ID  - MMO_2014_75_2_a6
ER  - 
%0 Journal Article
%A A. V. Domrin
%T Real-analytic solutions of the nonlinear Schr\"odinger equation
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2014
%P 205-218
%V 75
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a6/
%G ru
%F MMO_2014_75_2_a6
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/

[1] Zakharov V. E., Shabat A. B., “Tochnaya teoriya dvumernoi samofokusirovki i odnomernoi avtomodulyatsii voln v nelineinykh sredakh”, ZhETF, 61:1 (1971), 118–134

[2] Takhtadzhyan L. A., Faddeev L. D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[3] Akhmediev N. N., Ankevich A., Solitony. Nelineinye impulsy i puchki, Fizmatlit, M., 2003

[4] Osborne A. R., “Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation”, Nat. Hazards Earth Syst. Sci. Discuss., 2 (2014), 897–933 | DOI

[5] Smirnov A. O., Golovachev G. M., “Trekhfaznye resheniya nelineinogo uravneniya Shredingera v ellipticheskikh funktsiyakh”, Nelineinaya dinamika, 9:3 (2013), 389–407

[6] Domrin A. V., “Zadacha Rimana i matrichnoznachnye potentsialy so skhodyascheisya funktsiei Beikera–Akhiezera”, TMF, 144:3 (2005), 453–471 | DOI | MR | Zbl

[7] Domrin A. V., “Meromorfnoe prodolzhenie reshenii solitonnykh uravnenii”, Izv. RAN. Ser. matem., 74:3 (2010), 23–44 | DOI | MR | Zbl

[8] Cherednik I. V., “O regulyarnosti «konechnozonnykh» reshenii integriruemykh matrichnykh differentsialnykh uravnenii”, Dokl. AN SSSR, 266:3 (1982), 593–597 | MR | Zbl

[9] Gokhberg I. Ts., Krein M. G., “Sistemy integralnykh uravnenii na polupryamoi s yadrami, zavisyaschimi ot raznosti argumentov”, UMN, 13:2 (1958), 3–72 | MR | Zbl

[10] Domrin A. V., “Zamechaniya o lokalnom variante metoda obratnoi zadachi rasseyaniya”, Tr. MIAN, 253, 2006, 46–60 | MR

[11] Kalodzhero F., Degasperis A., Spektralnye preobrazovaniya i solitony. Metody resheniya i issledovaniya nelineinykh evolyutsionnykh uravnenii, Mir, M., 1985 | MR

[12] Its A. R., Rybin A. V., Sall M. A., “K voprosu o tochnom integrirovanii nelineinogo uravneniya Shredingera”, TMF, 74:1 (1988), 29–45 | MR | Zbl

[13] Hone A. N. W., “Crum transformation and rational solutions of the non-focusing nonlinear Schrödinger equation”, J. Phys. A, 30 (1997), 7473–7483 | DOI | MR | Zbl

[14] Domrin A. V., “O golomorfnykh resheniyakh uravnenii tipa Kortevega-de Friza”, Tr. MMO, 73, no. 2, 2012, 241–257 | Zbl

[15] Komlov A. V., “O polyusakh pikarovskikh potentsialov”, Tr. MMO, 71, 2010, 271–283

[16] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR

[17] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR