Conservation of phase space properties using exponential integrators on the cubic Schrodinger equation

    Authors

    H. Berland; A. L. Islas;C. M. Schober

    Comments

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    Abbreviated Journal Title

    J. Comput. Phys.

    Keywords

    exponential integrators; multisymplectic integrators; nonlinear spectral; diagnostics; nonlinear Schrodinger equation; SYMPLECTIC INTEGRATORS; RUNGE-KUTTA; CONSTRUCTION; SCHEMES; PDES; Computer Science, Interdisciplinary Applications; Physics, Mathematical

    Abstract

    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 Title

    Journal of Computational Physics

    Volume

    225

    Issue/Number

    1

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    284

    Last Page

    299

    WOS Identifier

    WOS:000248854300016

    ISSN

    0021-9991

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