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The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: Hamiltonian bifurcations in Schrodinger trimers
Author: Basarab, Casayndra H.
View Online: njit-etd2016-094
(ix, 68 pages ~ 0.7 MB pdf)
Department: Department of Mathematical Sciences
Degree: Doctor of Philosophy
Program: Mathematical Sciences
Document Type: Dissertation
Advisory Committee: Goodman, Roy (Committee chair)
Blackmore, Denis L. (Committee member)
Moore, Richard O. (Committee member)
Diekman, Casey (Committee member)
Gidea, Marian (Committee member)
Date: 2016-08
Keywords: Hamiltonian systems
Nonlinear dynamics
Nonlinear Schrodinger equation
Hamiltonian hopf bifurcation
Availability: Unrestricted

The phase space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom from three down to two. The families of standing waves are enumerated and normal forms are used to describe several families of relative periodic orbits whose topologies change due to Hamiltonian Hopf bifurcations and transcritical bifurcations. The Hamiltonian Hopf bifurcation occurs when eigenvalues on the imaginary axis collide and split and has two types: elliptic and hyperbolic. These two types arise in the DNLS problem, and the families of periodic orbits are discussed as a conserved quantity N is changed. The stability of each standing wave solution is discussed both numerically and analytically to describe how the dynamics change under perturbation of the parameter N.

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