Reduced order modeling is an important and fast-growing research field in computational
science and engineering, motivated by several reasons, of which we mention just a few …

In this work we employ a recently proposed bifurcation analysis technique, the deflated
continuation algorithm, to compute steady-state solitary waveforms in a one-component, two …

We study dynamical properties of the cubic lowest Landau level equation, which is used in
the modeling of fast rotating Bose–Einstein condensates. We obtain bounds on the decay of …

We consider the mean-field dynamics of Bose–Einstein condensates in rotating harmonic
traps and establish several stability and instability properties for the corresponding solution …

This work is concerned with the analysis and the development of efficient Reduced Order
Models (ROMs) for the numerical investigation of complex bifurcating phenomena held by …

We propose a computationally efficient framework to treat nonlinear partial differential
equations having bifurcating solutions as one or more physical control parameters are …

Motivated by experiments in atomic Bose–Einstein condensates (BECs), we compare
predictions of a system of ordinary differential equations (ODEs) for dynamics of one and two …

In this paper we consider stationary solutions to the nonlinear one-dimensional
Schrödinger equation with a periodic potential and a Stark-type perturbation. In the limit of …

The content of this thesis encapsulates four results in the analysis of nonlinear partial
differential equations of Schrödinger type. These mathematical models are motivated by …

EXISTENCE AND BIFURCATION OF PERIODIC SOLUTIONS IN SECOND ORDER
NONLINEAR SYSTEMS: BROUWER EQUIVARIANT DEGREE METHOD by Shi Yu A Page …