Abstract
In this paper, the idea of nonstandard finite difference discretization is employed to develop two variational integrators for the nonlinear Schrödinger equation with variable coefficients. These integrators are naturally multi-symplectic, and their multi-symplectic structures are presented by the multi-symplectic form formulas. Local truncation errors and convergences of the integrators are briefly discussed. The effectiveness and efficiency of the proposed schemes, such as the convergence order, numerical stability, and the capability in preserving the norm conservation, are verified in the numerical experiments.
Highlights
The nonlinear Schrödinger equation (NLSE) [, ]iut + uxx + V |u| u =, has wide applications in many areas such as quantum mechanics, nonlinear optics, and plasma physics, etc
4 Numerical simulations we report the performance of the nonstandard finite difference variational integrator ( ) for solving the nonlinear Schrödinger equation with variable coefficients ( )
We have considered the nonlinear Schrödinger equation with variable coefficients
Summary
In Section , we give some brief and necessary introductions to discrete variational integrators, the corresponding multi-symplectic form formulas, and the rules of nonstandard finite difference methods. In Section , with the triangle discretization and square discretization, we derive two discrete variational integrators for the NLS equation with variable coefficients ( ) based on nonstandard finite difference methods. We combine the advantages of nonstandard finite difference methods and discrete variational principles to construct multi-symplectic numerical schemes for the nonlinear Schrödinger equation with variable coefficients ( ).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
