Recurrence phase shift in Fermi–Pasta–Ulam nonlinear dynamics

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.

► The dynamics of FPU recurrence is associated with a phase shift between initial and final states. ► The properties of this phase shift are studied for the self-focussing NLS equation. ► This phase shift is a previously-unremarked feature of the FPU growth-return cycle. ► We anticipate its wide significance as an essential feature of related dynamics in other systems.