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This article is cited in 56 scientific papers (total in 56 papers)
Inverse scattering transform for the nonlocal reverse space–time nonlinear Schrödinger equation
M. J. Ablowitza, Bao-Feng Fengb, X. Luoc, Z. Musslimanid a Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO, USA
b School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, USA
c Department of Mathematics, State University of New York at Buffalo,
Buffalo, NY, USA
d Department of Mathematics, Florida State University,
Tallahassee, FL, USA
Abstract:
Nonlocal reverse space–time equations of the nonlinear Schrödinger (NLS) type were recently introduced. They were shown to be integrable infinite-dimensional dynamical systems, and the inverse scattering transform (IST) for rapidly decaying initial conditions was constructed. Here, we present the IST for the reverse space–time NLS equation with nonzero boundary conditions (NZBCs) at infinity. The NZBC problem is more complicated because the branching structure of the associated linear eigenfunctions is complicated. We analyze two cases, which correspond to two different values of the phase at infinity. We discuss special soliton solutions and find explicit one-soliton and two-soliton solutions. We also consider spatially dependent boundary conditions.
Keywords:
inverse scattering transform, nonlocal RST NLS equation.
Received: 24.08.2017
Citation:
M. J. Ablowitz, Bao-Feng Feng, X. Luo, Z. Musslimani, “Inverse scattering transform for the nonlocal reverse space–time nonlinear Schrödinger equation”, TMF, 196:3 (2018), 343–372; Theoret. and Math. Phys., 196:3 (2018), 1241–1267
Linking options:
https://www.mathnet.ru/eng/tmf9449https://doi.org/10.4213/tmf9449 https://www.mathnet.ru/eng/tmf/v196/i3/p343
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