High order explicit symplectic integrators for the Discrete Non Linear Schrödinger equation

Details High order explicit symplectic integrators for the Discrete Non Linear Schrödinger equation High order explicit symplectic integrators for the Discrete Non Linear Schrödinger equation

2010-12-15

arxiv.org/abs/1012.3242v1

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7, (1990), pp. 262.) we can construct high order numerical schemes, that result to be explicit methods and thus very fast. The performances of the integrators are discussed, studied as functions of the integration time step and compared with some non symplectic methods.

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