Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential

Document Type

Article

Publication Date

11-15-2017

Abstract

The nonlinear Schrödinger/Gross–Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. The problem is reduced to a finite-dimensional Hamiltonian system by a Galerkin truncation. Families of oscillatory orbits are sought in the neighborhoods of the system's nine branches of standing wave solutions. Normal forms are computed in the neighborhood of these branches’ various Hamiltonian Hopf and saddle–node bifurcations, showing how the oscillatory orbits change as a parameter is increased. Numerical experiments show agreement between normal form theory and numerical solutions to the reduced system and NLS/GP near the Hamiltonian Hopf bifurcations and some subtle disagreements near the saddle–node bifurcations due to exponentially small terms in the asymptotics.

Identifier

85028612300 (Scopus)

Publication Title

Physica D Nonlinear Phenomena

External Full Text Location

https://doi.org/10.1016/j.physd.2017.07.007

ISSN

01672789

First Page

39

Last Page

59

Volume

359

Grant

0807284

Fund Ref

National Science Foundation

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