Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation

Robert J. Deissler; Helmut R. Brand

doi:10.1103/PhysRevLett.72.478

Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation

Robert J. Deissler and Helmut R. Brand

Phys. Rev. Lett. 72, 478 – Published 24 January 1994

Abstract

We discuss time-dependent spatially localized solutions of the quintic complex Ginzburg-Landau equation applicable near a weakly inverted bifurcation to traveling waves. We find that there are—in addition to the stationary pulses reported previously—stable localized solutions that are periodic, quasiperiodic, or even chaotic in time. An intuitive picture for the stability of these time-dependent localized solutions is presented and the novelty of these phenomena in comparison to localized solutions arising for exactly integrable systems is emphasized.

Received 26 April 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.478

Authors & Affiliations

Robert J. Deissler and Helmut R. Brand

Center for Nonlinear Studies, MS-B 258, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545
Institute for Computational Mechanics in Propulsion (ICOMP), Ohio Aerospace Institute, NASA Lewis Research Center, 21000 Brookpark Road, Cleveland, Ohio 44135
Theoretische Physik III, Universität Bayreuth, Postfach 101251, D-95440 Bayreuth, Germany