Geodesic
Inverse scattering transform for the~nonlocal reverse space--time nonlinear Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 3, pp. 343-372

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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
Mots-clés : nonlocal RST NLS equation. 
@article{TMF_2018_196_3_a0,
     author = {M. J. Ablowitz and Bao-Feng Feng and X. Luo and Z. Musslimani},
     title = {Inverse scattering transform for the~nonlocal reverse space--time nonlinear {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {343--372},
     publisher = {mathdoc},
     volume = {196},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_196_3_a0/}
}
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M. J. Ablowitz; Bao-Feng Feng; X. Luo; Z. Musslimani. Inverse scattering transform for the~nonlocal reverse space--time nonlinear Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 3, pp. 343-372. http://geodesic.mathdoc.fr/item/TMF_2018_196_3_a0/