Conservation of phase space properties using exponential integrators on the cubic Schrodinger equation
Abbreviated Journal Title
J. Comput. Phys.
exponential integrators; multisymplectic integrators; nonlinear spectral; diagnostics; nonlinear Schrodinger equation; SYMPLECTIC INTEGRATORS; RUNGE-KUTTA; CONSTRUCTION; SCHEMES; PDES; Computer Science, Interdisciplinary Applications; Physics, Mathematical
The cubic nonlinear Schrodinger (NLS) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The "nonlinear" spectrum of the associated Lax pair reveals topological properties of the NLS phase space that are difficult to assess by other means. In this paper we use the invariance of the nonlinear spectrum to examine the long time behavior of exponential and multisymplectic integrators as compared with the most commonly used split step approach. The initial condition used is a perturbation of the unstable plane wave solution, which is difficult to numerically resolve. Our findings indicate that the exponential integrators from the viewpoint of efficiency and speed have an edge over split step, while a lower order multisymplectic is not as accurate and too slow to compete. (c) 2006 Elsevier Inc. All rights reserved.
Journal of Computational Physics
"Conservation of phase space properties using exponential integrators on the cubic Schrodinger equation" (2007). Faculty Bibliography 2000s. 6867.