Conservative local discontinuous Galerkin methods for the cubic-quintic nonlinear Schrödinger equation

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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 languageEnglish (US)
Article number165821
JournalOptik
Volume226
DOIs
StatePublished - 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

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