Reduced-order modeling for Ablowitz-Ladik equation

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