Recurrence phase shift in Fermi–Pasta–Ulam nonlinear dynamics

Article history: Received 22 September 2011 Accepted 4 October 2011 Available online 7 October 2011 Communicated by V.M. Agranovich We show that the dynamics of Fermi–Pasta–Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schrödinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi–Pasta–Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.