Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions
By Mark J. Ablowitz, Xu‐Dan Luo, Ziad Musslimani. 2016
204 citations recorded by the source corpus.
In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrodinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which...
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/77a89c74e3ba4819fdfa7f2bee91cc1f56c479dc
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data (2021, methodology): “1a) is a compatibility condition of the following two linear equations (Lax pair) [3, 4] { Φx + ikσ3Φ = U(x, t)Φ Φt + 2ik σ3Φ = V (x, t, k)Φ (2.”