We use Jacobi coordinates and a momentum map/Lie-Poisson reduction to derive a system of equations for the three-vortex problem with no coordinate singularities and use it to …
We show via analytical perturbation theory that the leapfrogging vortex quartet becomes unstable exactly at the critical ratio $\alpha= \phi^{-2}.$
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as _leapfrogging_ orbits. These solutions, which consists of two pairs …
When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a certain constraint, the nonlinear Schrödinger …
We consider the bifurcations of standing wave solutions to the nonlinear Schrödinger equation (NLS) posed on a quantum graph consisting of two loops connected by a single edge, the …
The nonlinear Schrödinger/Gross--Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. The problem is reduced to a finite-dimensional …
We study the long-time behavior of solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation (NLS/GP) with a symmetric double-well potential. NLS/GP governs …
We examine the dynamics of solutions to nonlinear Schrödinger/Gross-- Pitaevskii equations that arise due to semisimple indefinite Hamiltonian Hopf bifurcations---the collision of …
Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled …