Related papers: Singularly Perturbed Boundary-Equilibrium Bifurcat…
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial…
It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by the interplay of the cubic attractive nonlinearity and spin-orbit coupling (SOC) in binary Bose-Einstein condensates. We introduce a…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase…
The cyclicity problem, crucial in analyzing planar vector fields, consists in estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in…
In this work, we consider quasi-one-dimensional Bose-Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double well potentials. In particular, we study a setup in which such a 'collisionally…
We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength g = 2 of the nonlinear repulsion between the components, and linear coupling…
Nonsmooth formulations of physical models are common, particularly in climate modeling. However, in many of these models, there is little justification for this modeling choice, and no mathematical indication that the resulting behavior in…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…
Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called "shrinking points". In this paper we extend…
In 2D topological systems chiral edges may exhibit a spectral change due to the formation of a Bose condensate and partial confinement in the bulk according to the topological symmetry breaking (TSB) mechanism. We analyze in detail what…
We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios,…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
Two primary types of numerical instabilities often occur in low-order finite element method (FEM) analyses of thermo-hydro-mechanical (THM) phenomena: (1) pressure oscillations arising improper interpolation of pressure and displacement…
We reanalyze the non-linear population dynamics of a Bose-Einstein Condensate (BEC) in a double well trap considering a semiclassical approach based on a time dependent variational principle applied to coherent states associated to SU(2)…
This research focuses on the interesting physical phenomenon of the bead-hoop system. The bifurcation can be observed investigating the equilibrium point of the bead, and nonlinear oscillation also occurs from the bead's motion. This paper…
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of…
We study effects of the spontaneous symmetry-breaking (SSB) in solitons built of the dipolar Bose-Einstein condensate (BEC), trapped in a dual-core system with the dipole-dipole interactions (DDIs) and hopping between the cores. Two…