Document Type
Dissertation
Date of Award
Summer 8-31-2016
Degree Name
Doctor of Philosophy in Mathematical Sciences - (Ph.D.)
Department
Mathematical Sciences
First Advisor
Roy Goodman
Second Advisor
Denis L. Blackmore
Third Advisor
Richard O. Moore
Fourth Advisor
Casey Diekman
Fifth Advisor
Marian Gidea
Abstract
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.
Recommended Citation
Basarab, Casayndra H., "Hamiltonian bifurcations in Schrodinger trimers" (2016). Dissertations. 87.
https://digitalcommons.njit.edu/dissertations/87
