Bifurcation

Transition to instability of the leapfrogging vortex quartet
We show via analytical perturbation theory that the leapfrogging vortex quartet becomes unstable exactly at the critical ratio $\alpha= \phi^{-2}.$
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Transition to instability of the leapfrogging vortex quartet
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
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
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
Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes
We examine the dynamics of solutions to nonlinear Schrödinger/Gross– Pitaevskii equations that arise due to semisimple indefinite …
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Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes
Stability and instability of nonlinear defect states in the coupled mode equations---analytical and numerical study
Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg …
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Stability and instability of nonlinear defect states in the coupled mode equations---analytical and numerical study