General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

Abstract

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.

26 pages, 3 figures

References in corpus (10)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Alice-Bob Physics: Coherent Solutions of Nonlocal KdV Systems
• Nonlocal Nonlinear Schrödinger Equations and Their Soliton Solutions
• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrodinger equation
• Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential
• Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Nonlocal Fordy - Kulish Equations on Symmetric Spaces
• Nonstandard bilinearization of $\mathcal{P}\mathcal{T}$-invariant nonlocal nonlinear Schrödinger equation: Bright soliton solutions

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