Abstract:
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.
Citation:
A. V. Domrin, “Real-analytic solutions of the nonlinear Schrödinger equation”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 205–218; Trans. Moscow Math. Soc., 75 (2014), 173–183
This publication is cited in the following 8 articles:
A. B. Khasanov, Kh. N. Normurodov, U. O. Hudayerov, “Integrating the modified Korteweg–de Vries–sine-Gordon equation in the class of periodic infinite-gap functions”, Theoret. and Math. Phys., 214:2 (2023), 170–182
A. Khasanov, R. Eshbekov, Kh. Normurodov, “Integration of a Nonlinear Hirota Type Equation with Finite Density in the Class of Periodic Functions”, Lobachevskii J Math, 44:10 (2023), 4329
Vsevolod Zh. Sakbaev, “Flows in infinite-dimensional phase space equipped with a finitely-additive invariant measure”, Mathematics, 11:5 (2023), 1161–49
U. B. Muminov, A. B. Khasanov, “Integration of a defocusing nonlinear Schrödinger equation with additional terms”, Theoret. and Math. Phys., 211:1 (2022), 514–531
U. B. Muminov, A. B. Khasanov, “Zadacha Koshi dlya defokusiruyuschego nelineinogo uravneniya Shredingera s nagruzhennym chlenom”, Matem. tr., 25:1 (2022), 102–133
U. B. Muminov, A. B. Khasanov, “The Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with a Loaded Term”, Sib. Adv. Math., 32:4 (2022), 277
A. V. Domrin, M. A. Shumkin, B. I. Suleimanov, “Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type”, Journal of Mathematical Physics, 63:2 (2022)
G. A. Mannonov, A. B. Khasanov, “The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions”, St. Petersburg Math. J., 34:5 (2023), 821–845
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