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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
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
High-Order Bisection Method for Computing Invariant Manifolds of Two-Dimensional Maps
We describe an efficient and accurate numerical method for computing smooth approximations to invariant manifolds of planar maps, based …
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High-Order Bisection Method for Computing Invariant Manifolds of Two-Dimensional Maps
Nonlinear hydrodynamic phenomena in Stokes flow regime
We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a …
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Nonlinear hydrodynamic phenomena in Stokes flow regime
Chaotic scattering in solitary wave interactions: A singular iterated-map description
We derive a family of singular iterated maps—closely related to Poincaré maps—that describe chaotic interactions between …
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Chaotic scattering in solitary wave interactions: A singular iterated-map description
Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation
We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a …
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Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation
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
Chaotic Scattering and the n-bounce Resonance in Solitary Wave Interactions
We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary wave collisions. In these …
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Chaotic Scattering and the $n$-bounce Resonance in Solitary Wave Interactions
Kink-antikink collisions in the ϕ4 equation: The n-bounce resonance and the separatrix map
We provide a detailed mathematical explanation of a phenomenon known as the two-bounce resonance observed in collisions between kink …
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Kink-antikink collisions in the $\phi^4$ equation: The $n$-bounce resonance and the separatrix map
Trapping light with grating defects
Gap solitons are localized traveling waves that exist in Bragg grating optical fibers. We demonstrate a family of grating defects that …
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