Abstract:
Asymptotics at t→+∞ of the solution of the nonlinear Schrödinger equation is investigated by means of the inverse scattering method in the case of initial data tending rapidly at x→±∞ to different one-gap potentials.
Citation:
R. F. Bikbaev, “Large-time asymptotics of the solution of the nonlinear Schrödinger equation with boundary conditions of step type”, TMF, 81:1 (1989), 3–11; Theoret. and Math. Phys., 81:1 (1989), 1011–1017
This publication is cited in the following 16 articles:
A. B. Khasanov, T. G. Khasanov, “The Cauchy Problem for the Nonlinear Complex Modified Korteweg-de Vries Equation with Additional Terms in the Class of Periodic Infinite-Gap Functions”, Sib Math J, 65:4 (2024), 846
A. B. Khasanov, T. G. Khasanov, “Zadacha Koshi dlya nelineinogo kompleksnogo modifitsirovannogo uravneniya Kortevega — de Friza (kmKdF) s dopolnitelnymi chlenami v klasse periodicheskikh beskonechnozonnykh funktsii”, Sib. matem. zhurn., 65:4 (2024), 735–759
Thierry Laurens, “Global Well-Posedness for H−1(R) Perturbations of KdV with Exotic Spatial Asymptotics”, Commun. Math. Phys., 397:3 (2023), 1387
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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
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R. F. Bikbaev, “Shock waves in the modified Korteweg-de Vries-Burgers equation”, J Nonlinear Sci, 5:1 (1995), 1
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G.A. El, V.V. Geogjaev, A.V. Gurevich, A.L. Krylov, “Decay of an initial discontinuity in the defocusing NLS hydrodynamics”, Physica D: Nonlinear Phenomena, 87:1-4 (1995), 186
B. M. Levitan, A. B. Khasanov, “Estimation of the Cauchy function for finite-zone nonperiodic potentials”, Funct. Anal. Appl., 26:2 (1992), 91–98
R. F. Bikbaev, “Finite-gap attractors and transition processes of the shock wave type in integrable systems”, J. Math. Sci., 77:2 (1995), 3033–3041
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