Conservación de invariantes de la ecuación de Schrödinger no lineal por el método LDG

Authors

  • P. E. Castillo Departamento de Ciencias Matemáticas Universidad de Puerto Rico.
  • S. A. Gómez Departamento de Ciencias Matemáticas Universidad de Puerto Rico.

DOI:

https://doi.org/10.31349/RevMexFisE.64.52

Keywords:

Nonlinear Schr¨odinger equation, Local Discontinuous Galerkin method, energy and Hamiltonian conservation, modified Crank- Nicolson.

Abstract

Conservation of the energy and the Hamiltonian of a general non linear Schr¨odinger equation is analyzed for the finite element method “Local Discontinuous Galerkin” spatial discretization. Conservation of the discrete analogue of these quantities is also proved for the fully discrete problem using the modified Crank-Nicolson method as time marching scheme. The theoretical results are validated on a series of problems
for different nonlinear potentials.

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Published

2018-04-10