Reduced-order modeling for Ablowitz–Ladik equation

Murat Uzunca and Bülent Karasözen

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 213, issue C, 261-273

Abstract: In this paper, reduced-order models (ROMs) are constructed for the Ablowitz–Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schrödinger equation (NLSE) with and without damping. Both ALEs are non-canonical conservative and dissipative Hamiltonian systems with the Poisson matrix depending quadratically on the state variables, and with quadratic Hamiltonian. The full-order solutions are obtained with the energy preserving midpoint rule for the conservative ALE and exponential midpoint rule for the dissipative ALE. The reduced-order solutions are constructed intrusively by preserving the skew-symmetric structure of the reduced non-canonical Hamiltonian system by applying proper orthogonal decomposition (POD) with the Galerkin projection. For an efficient offline–online decomposition of the ROMs, the quadratic nonlinear terms of the Poisson matrix are approximated by the discrete empirical interpolation method (DEIM). The computation of the reduced-order solutions is further accelerated by the use of tensor techniques. Preservation of the Hamiltonian and momentum for the conservative ALE, and preservation of dissipation properties of the dissipative ALE, guarantee the long-term stability of soliton solutions.

Keywords: Hamiltonian systems; Nonlinear Schrödinger equation; Proper orthogonal decomposition; Discrete empirical interpolation; Tensors (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475423002677
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:213:y:2023:i:c:p:261-273

DOI: 10.1016/j.matcom.2023.06.013

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().