Integrable nonlocal nonlinear Schrödinger equation.

By Mark J. Ablowitz, Ziad Musslimani. Physical Review Letters, 2013

778 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5f68b919d3c42edfee056b4ef7321fd1957f6e63

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Complete integrability of Nonlocal Nonlinear Schr\"odinger equation (2015, methodology): “The soliton in [3] however was derived assuming that a(λ) has only one simple zero which is purely imaginary, thus violating condition C2.”
Nonlinear waves in PT -symmetric systems (2016, positive): “Ablowitz and Musslimani (2013) considered yet another reduction, φ(x, t) = ±ψ∗(−x, t) leading to the equation with nonlocal nonlinearity (σ = ±1) iψt(x, t) = ψxx(x, t) + 2σψ(x, t)ψ ∗(−x, t)ψ(x, t).”
Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations (2017, methodology): “ waves, which are periodic in x direction and localized in y direction on the (x;y)-plane. Although these soliton solutions 3 also have singularities as soliton solutions of the nonlocal NLS equation [21], but general nbreather solutions for the x-nonlocal DS equations can be generated by the follow”
Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data (2021, neutral): “Musslimani in [5].”
Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions (2016, background): “1) iqt(x, t) = qxx(x, t)− 2σq(2)(x, t)q(−x, t), where q(x, t) denotes complex conjugate of q(x, t), x ∈ R, t ≥ 0 and σ = ∓1, has been developed in [1, 3].”
General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions (2017, methodology): “led NLS, as well as their semi-discrete analogues [60]–[70]. Moreover, the IST to solve the initial-value problem with vanishing boundary condition for the nonlocal NLS equation has been developed in [17, 21, 22]. For pure soliton solutions corresponding to reﬂectionless potentials, one obtains one-”
High-order soliton matrices for Sasa–Satsuma equation via local Riemann–Hilbert problem (2019, methodology): “Recently, a detailed study of the inverse scattering theory for the integrable nonlocal NLS equation is presented using a new left–right Riemann–Hilbert problem and the Cauchy problem is formulated [32,33].”