Dbar-approach to coupled nonlocal NLS equation and general nonlocal Reduction
Xueru Wang, Junyi Zhu
TL;DR
This paper introduces a Dbar-method approach to analyze the coupled nonlocal NLS equation, deriving explicit solutions and conservation laws, and explores its reduction to the nonlocal NLS equation.
Contribution
It develops a novel Dbar-problem framework for coupled nonlocal NLS equations and extends the spatial transform method for their analysis.
Findings
Explicit solutions for the coupled nonlocal NLS equation
Conservation laws derived for the system
Detailed discussion on nonlocal reduction
Abstract
The coupled nonlocal NLS equation is studied by virtue of the Dbar-problem. Two spectral transform matrices are introduced to define two associated Dbar-problems. The relations between the coupled nonlocal NLS potential and the solution of the Dbar-problem are constructed. The spatial transform method is extended to obtain the coupled nonlocal NLS equation and its conservation laws. The general nonlocal reduction of the coupled nonlocal NLS equation to the nonlocal NLS equation is discussed in detail. The explicit solutions are derived.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Quantum Mechanics and Non-Hermitian Physics