Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Discrete Solitons And Vortices In Anisotropic Hexagonal And Honeycomb Lattices, Q E. Hoq, Panayotis G. Kevrekidis, A R. Bishop
Discrete Solitons And Vortices In Anisotropic Hexagonal And Honeycomb Lattices, Q E. Hoq, Panayotis G. Kevrekidis, A R. Bishop
Mathematics and Statistics Department Faculty Publication Series
In the present work, we consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. We quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation …
Non-Conservative Variational Approximation For Nonlinear Schrödinger Equations., J. Rossi, R. Carretero-González, P. G. Kevrekidis
Non-Conservative Variational Approximation For Nonlinear Schrödinger Equations., J. Rossi, R. Carretero-González, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Recently, Galley [Phys. Rev. Lett. 110, 174301 (2013)] proposed an initial value problem formulation of Hamilton’s principle applied to non-conservative systems. Here, we explore this formulation for complex partial differential equations of the nonlinear Schrödinger (NLS) type, examining the dynamics of the coherent solitary wave structures of such models by means of a non-conservative variational approximation (NCVA). We compare the formalism of the NCVA to two other variational techniques used in dissipative systems; namely, the perturbed variational approximation and a generalization of the so-called Kantorovich method. All three variational techniques produce equivalent equations of motion for the perturbed NLS models …
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Mathematics and Statistics Department Faculty Publication Series
For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas-Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one dimensional amplitude equation that describes the slow …