A novel method for simulating the complex Ginzburg-Landau equation
- 1 June 1995
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 53 (2) , 315-333
- https://doi.org/10.1090/qam/1330655
Abstract
We present a split-step method for integration of the complex Ginzburg-Landau equation in any number of spatial dimensions. The novel aspect of the method lies in the fact that each portion of the splitting is explicitly integrable. This leads to an extremely fast, stable, and efficient procedure. A comparison is made with spectral and pseudospectral procedures which have appeared in the literature.Keywords
This publication has 16 references indexed in Scilit:
- Construction of higher order symplectic integratorsPublished by Elsevier ,2002
- The accuracy of symplectic integratorsNonlinearity, 1992
- On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equationPhysica D: Nonlinear Phenomena, 1990
- Hard turbulence in a finite dimensional dynamical system?Physics Letters A, 1989
- A form of turbulence associated with defectsPhysica D: Nonlinear Phenomena, 1989
- Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equationJournal of Computational Physics, 1984
- Calculation of transverse effects in optical bistability using fast Fourier transform techniquesOptics Communications, 1982
- Nonlinear-optical calculations using fast-transform methods: Second-harmonic generation with depletion and diffractionPhysical Review A, 1980
- Simultaneous forward and backward integration for standing waves in a resonatorApplied Optics, 1979
- Recurrence of Nonlinear Ion Acoustic WavesPhysical Review Letters, 1972