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Symplectic methods for the nonlinear Schrödinger equation

✍ Scribed by Y.-F. Tang; L. Vázquez; F. Zhang; V.M. Pérez-García

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
528 KB
Volume
32
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper, we show that the spatial discretization of the nonlinear SchrSdinger equation leads to a Hamiltonian system, which can be simulated with symplectic numerical schemes.

In particular, we apply two symplectic integrators to the nonlinear SchrSdinger equation, and we demonstrate that they are able to produce accurate results and to preserve very well the invariants of the original system, such as the energy and charge.

📜 SIMILAR VOLUMES

Geometric Integrators for the Nonlinear
Geometric Integrators for the Nonlinear Schrödinger Equation
✍ A.L. Islas; D.A. Karpeev; C.M. Schober 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 270 KB

Recently an interesting new class of PDE integrators, multisymplectic schemes, has been introduced for solving systems possessing a certain multisymplectic structure. Some of the characteristic features of the method are its local nature (independent of boundary conditions) and an equal treatment of