Work

Integrable nonlocal finite-dimensional Hamiltonian systems related to the Ablowitz-Kaup-Newell-Segur system

Year: 2024

Type: article

Abstract: The method of nonlinearization of the Lax pair is developed for the Ablowitz-Kaup-Newell-Segur (AKNS) equation in the presence of space-inverse reductions. As a result, we obtain a new type of finite-dimensional Hamiltonian systems: they are nonlocal in the sense that the inverse of the space variable is involved. For such nonlocal Hamiltonian systems, we show that they preserve the Liouville integrability and they can be linearized on the Jacobi variety. We also show how to construct the algebro-geometric solutions to the AKNS equation with space-inverse reductions by virtue of our nonlocal finite-dimensional Hamiltonian systems. As an application, algebro-geometric solutions to the AKNS equation with the Dirichlet and with the Neumann boundary conditions, and algebro-geometric solutions to the nonlocal nonlinear Schrödinger (NLS) equation are obtained. nonlocal finite-dimensional integrable Hamiltonian system, algebro-geometric solution, Dirichlet (Neumann) boundary, nonlocal NLS equation.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0200162

Authors: Baoqiang Xia, Ruguang Zhou

Institution: Jiangsu Normal University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G3968746056, G7417850282