Abstract
In this paper, we propose the local discontinuous Galerkin methods to solve the cubic-quintic nonlinear Schrödinger equation. Our numerical methods are based on the local discontinuous Galerkin methods in space and Crank-Nicholson method in time. By choosing the appropriate numerical fluxes, we can prove the mass- and energy-conserving properties for both the semi-discrete and fully discrete methods. We also present some numerical experiments, including soliton with linear potential and with time sinusoidal modulated potential, to demonstrate the accuracy and mass- and energy-conserving properties of our proposed methods.
Original language | English (US) |
---|---|
Article number | 165821 |
Journal | Optik |
Volume | 226 |
DOIs | |
State | Published - Jan 2021 |
Keywords
- Crank-Nicholson method
- Cubic-quintic nonlinear Schrödinger equation
- Energy conservation
- Local discontinuous Galerkin
- Mass conservation
- Soliton solutions
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Electrical and Electronic Engineering