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math.NA2024★ 6 cited
A Finite Difference Scheme for (2+1)D Cubic-Quintic Nonlinear Schrödinger Equations with Nonlinear Damping
Anh Ha Le, Toan T. Huynh, Quan M. Nguyen
Solitons of the purely cubic nonlinear Schrödinger equation in a space dimension of suffer critical and supercritical collapses. These solitons can be stabilized in a cu…
math.NA2023★ 8 cited
Analysis of a Crank-Nicolson finite difference scheme for (2+1)D perturbed nonlinear Schrödinger equations with saturable nonlinearity
Anh-Ha Le, Toan T. Huynh, Quan M. Nguyen
We analyze a Crank-Nicolson finite difference discretization for the perturbed (2+1)D nonlinear Schrödinger equation with saturable nonlinearity and a perturbation of cubic loss. W…