1,182 research outputs found
Propagating Wave Patterns in a Derivative Nonlinear Schr\"odinger System with Quintic Nonlinearity
Exact expressions are obtained for a diversity of propagating patterns for a
derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These
patterns include bright pulses, fronts and dark solitons. The evolution of the
wave envelope is determined via a pair of integrals of motion, and reduction is
achieved to Jacobi elliptic cn and dn function representations. Numerical
simulations are performed to establish the existence of parameter ranges for
stability. The derivative quintic nonlinear Schr\"odinger model equations
investigated here are important in the analysis of strong optical signals
propagating in spatial or temporal waveguides.Comment: J. Phys. Soc. Jpn. in pres
Intrinsic localized modes in parametrically driven arrays of nonlinear resonators
We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schrödinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory
Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations
We prove the most general theorem about spectral stability of multi-site
breathers in the discrete Klein-Gordon equation with a small coupling constant.
In the anti-continuum limit, multi-site breathers represent excited
oscillations at different sites of the lattice separated by a number of "holes"
(sites at rest). The theorem describes how the stability or instability of a
multi-site breather depends on the phase difference and distance between the
excited oscillators. Previously, only multi-site breathers with adjacent
excited sites were considered within the first-order perturbation theory. We
show that the stability of multi-site breathers with one-site holes change for
large-amplitude oscillations in soft nonlinear potentials. We also discover and
study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site
breathers in soft quartic potentials near the points of 1:3 resonance.Comment: 34 pages, 12 figure
Exceptional points for photon pairs bound by nonlinear dissipation in cavity arrays
We study theoretically the dissipative Bose-Hubbard model describing array of
tunneling-coupled cavities with non-conservative photon-photon interaction. Our
calculation of the complex energy spectrum for the photon pairs reveals
exceptional points where the two-photon states bound by nonlinear dissipation
are formed. This improves fundamental understanding of the interplay of
non-Hermiticity and interactions in the quantum structures and can be
potentially used for on-demand nonlinear light generation in photonic lattices.Comment: 4 pages, 4 figure
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