Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation

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Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data (2021, methodology): “Typical examples are the reverse space-time nonlocal NLS equation and the reverse time nonlocal NLS equation, the complex/real space-time SineGordon equation, the complex/real reverse space-time mKdV equation [1, 6, 7], the nonlocal derivative NLS equation [39], and the multidimensional nonlocal Dav”
Integrable Nonlocal Nonlinear Equations (2016, methodology): “An extension to a (2 + 1) dimensional integrable nonlocal NLS type equations was subsequently analyzed in [24].”
Transformations between Nonlocal and Local Integrable Equations (2017, background): “Consider the PT -symmetric DS equations [12, 15] iAt(x, y, t) = Axx(x, y, t) + σ (2)Ayy(x, y, t) + [ A(x, y, t)A ∗(−x,−y, t)− 2Q(x, y, t)]A(x, y, t), Qxx(x, y, t)− σ(2)Qyy(x, y, t) = [A(x, y, t)A∗(−x,−y, t)]xx , (II.”
Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations (2017, methodology): “evitable and worthwhile, such as the integrable models and nonlinear waves in this system. Corresponding author: hejingsong@nbu.edu.cn, jshe@ustc.edu.cn. 1 arXiv:1704.06792v1 [nlin.SI] 22 Apr 2017 In [19] Fokas, and in [20] Ablowitz and Musslimani, introduced the following nonlocal DS equation iA t=”