Details

Autor(en) / Beteiligte

• Ablowitz, M. J.
• Feng, Bao-Feng
• Luo, Xu-Dan
• Musslimani, Z. H.

Titel

Inverse Scattering Transform for the Nonlocal Reverse Space–Time Nonlinear Schrödinger Equation

Ist Teil von

• Theoretical and mathematical physics, 2018-09, Vol.196 (3), p.1241-1267

Ort / Verlag

Moscow: Pleiades Publishing

Erscheinungsjahr

2018

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.