87 research outputs found
Moving Embedded Solitons
The first theoretical results are reported predicting {\em moving} solitons
residing inside ({\it embedded} into) the continuous spectrum of radiation
modes. The model taken is a Bragg-grating medium with Kerr nonlinearity and
additional second-derivative (wave) terms. The moving embedded solitons (ESs)
are doubly isolated (of codimension 2), but, nevertheless, structurally stable.
Like quiescent ESs, moving ESs are argued to be stable to linear approximation,
and {\it semi}-stable nonlinearly. Estimates show that moving ESs may be
experimentally observed as 10 fs pulses with velocity th that
of light.Comment: 9 pages 2 figure
Embedded Solitons in a Three-Wave System
We report a rich spectrum of isolated solitons residing inside ({\it embedded
} into) the continuous radiation spectrum in a simple model of three-wave
spatial interaction in a second-harmonic-generating planar optical waveguide
equipped with a quasi-one-dimensional Bragg grating. An infinite sequence of
fundamental embedded solitons are found, which differ by the number of internal
oscillations. Branches of these zero-walkoff spatial solitons give rise,
through bifurcations, to several secondary branches of walking solitons. The
structure of the bifurcating branches suggests a multistable configuration of
spatial optical solitons, which may find straightforward applications for
all-optical switching.Comment: 5 pages 5 figures. To appear in Phys Rev
Thirring Solitons in the presence of dispersion
The effect of dispersion or diffraction on zero-velocity solitons is studied
for the generalized massive Thirring model describing a nonlinear optical fiber
with grating or parallel-coupled planar waveguides with misaligned axes. The
Thirring solitons existing at zero dispersion/diffraction are shown numerically
to be separated by a finite gap from three isolated soliton branches. Inside
the gap, there is an infinity of multi-soliton branches. Thus, the Thirring
solitons are structurally unstable. In another parameter region (far from the
Thirring limit), solitons exist everywhere.Comment: 12 pages, Latex. To appear in Phys. Rev. Let
Bifurcation of Limit Cycles from Boundary Equilibria in Impacting Hybrid Systems
A semianalytical method is derived for finding the existence and stability of single-impact periodicorbits born in a boundary equilibrium bifurcation in a generaln-dimensional impacting hybridsystem. Known results are reproduced for planar systems and general formulae derived for three-dimensional (3D) systems. A numerical implementation of the method is illustrated for several 3Dexamples and for an 8D wing-flap model that shows coexistence of attractors. It is shown how themethod can easily be embedded within numerical continuation, and some remarks are made aboutnecessary and sufficient conditions in arbitrary dimensional system
Wave-pinned patterns for cell polarity — a catastrophe theory explanation
A class of four-component reaction-diffusion systems are studied in one spatial dimension, with one of four specific reaction kinetics. Models of this type seek to capture the interaction between active and inactive forms of two G-proteins, known as ROPs in plants, thought to underly cellular polarity formation. The systems conserve total concentration of each ROP, which enables reduction to simple canonical forms when one seeks conditions for homogeneous equilibria or heteroclinic connections between them. Transitions between different multiplicities of such states are classified using a novel application of catastrophe theory. For the time-dependent problem, the heteroclinic connections represent so-called wave-pinned states that separate regions of the domain with different ROP concentrations. It is shown numerically how the form of wave-pinning reached can be predicted as a function of the domain size and initial total ROP concentrations. This leads to state diagrams of different polarity forms as a function of total concentrations and system parameters
Normal form analysis of bouncing cycles in isotropic rotor stator contact problems
This work considers analysis of sustained bouncing responses of rotating shafts with nonlinear lateral vibrations due to rotor stator contact. The insight that this is an internal resonance phenomena makes this an ideal system to be studied with the method of normal forms, which assumes that a system may be modelled primarily in terms of just its resonant response components. However, the presence of large non smooth nonlinearities due to impact and rub mean that the method must be extended. This is achieved here by incorporating an alternating frequency/time (AFT) step to capture nonlinear forces. Furthermore, the presence of gyroscopic terms leads to the need to handle complex modal variables, and a rotating coordinate frame must be used to obtain periodic responses. The process results in an elegant formulation that can provide reduced order models of a wide variety of rotor systems, with potentially many nonlinear degrees of freedom. The method is demonstrated by comparing against time simulation of two example rotors, demonstrating high precision on a simple model and approximate precision on a larger model
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