General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
By B. Feng, Xu‐Dan Luo, Mark J. Ablowitz, Ziad Musslimani. Nonlinearity, 2017
197 citations recorded by the source corpus.
General soliton solutions to a nonlocal nonlinear Schrödinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions are considered via the combination of Hirota’s bilinear method and the Kadomtsev–Petviashvili (KP) hierarchy reduction method. First, general N-soliton solutions with zero boundary conditions are constructed. Starting from the tau functions of the two-component KP hierarchy, it is shown that they can be expressed in terms of either Gramian or double Wronskian determinants. On the contrary, from the tau functions of single component KP hierarchy, general soliton solutions to the nonlocal NLS equation with nonzero boundary conditions are obtained. All possible soliton solutions to nonlocal NLS with Parity (PT)-symmetry for both zero and nonzero boundary conditions are found in the present paper.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/83e5ef2ceba0219fe3f262282bd294052be3c4e0
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): “3) where q0 > 0, α ∈ R, 0 ≤ θ± < 2π, is considered in [4], where the IST method is developed and the soliton solutions are constructed for certain values of the parameters θ± (see also [2], where the general N -soliton solutions are presented).”