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Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as leapfrogging orbits. …
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Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach
Drift of spectrally stable shifted states on star graphs
When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a …
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Drift of spectrally stable shifted states on star graphs
Topological features determining the error in the inference of networks using transfer entropy
The problem of inferring interactions from observations of individual behavior in networked dynamical systems is ubiquitous in science …
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Topological features determining the error in the inference of networks using transfer entropy
Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model
We analyze the fractal structure seen in kink-antikink collisions of the $\varphi^4$ equation. The analysis is based on qualitative …
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Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model
NLS bifurcations on the bowtie combinatorial graph and the dumbbell metric graph
We consider the bifurcations of standing wave solutions to the nonlinear Schrödinger equation (NLS) posed on a quantum graph consisting …
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NLS bifurcations on the bowtie combinatorial graph and the dumbbell metric graph
Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential
The nonlinear Schrödinger/Gross–Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. …
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Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential
A Mechanical Analog of the Two-Bounce Resonance of Solitary Waves: Modeling and Experiment
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known …
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A Mechanical Analog of the Two-Bounce Resonance of Solitary Waves: Modeling and Experiment
Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates
We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary …
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Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates
Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii Equation
We study the long-time behavior of solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation (NLS/GP) with a symmetric …
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Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii Equation
High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps
An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical …
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High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps