17 research outputs found
Phase Locking Between Fiske and Flux-Flow Modes in Coupled Sine-Gordon Systems
We investigate nonlinear resonant modes in coupled sine-Gordon systems with open boundary conditions. The system models coupled Josephson junctions with boundary conditions representing the situation where an external magnetic field is applied. The so-called Fiske modes are found to exist in phase-locked states where the equivalent voltages across the individual coupled Josephson junctions are either identical or identical with opposite signs. The analysis covers all Fiske modes including the flux-flow region. We present a comprehensive comparison between results on analytical treatment and direct numerical simulations of the coupled field equations
Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities
A class of discrete nonlinear Schrodinger equations with arbitrarily high
order nonlinearities is introduced. These equations are derived from the same
Hamiltonian using different Poisson brackets and include as particular cases
the saturable discrete nonlinear Schrodinger equation and the Ablowitz-Ladik
equation. As a common property, these equations possess three kinds of exact
analytical stationary solutions for which the Peierls-Nabarro barrier is zero.
Several properties of these solutions, including stability, discrete breathers
and moving solutions, are investigated
Statistical mechanics of a discrete SchroĚdinger equation with saturable nonlinearity
We study the statistical mechanics of the one-dimensional discrete nonlinear
Schr\"odinger (DNLS) equation with saturable nonlinearity. Our study represents
an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding
the statistical mechanics of the one-dimensional DNLS equation with a cubic
nonlinearity. As in this earlier study we identify the spontaneous creation of
localized excitations with a discontinuity in the partition function. The fact
that this phenomenon is retained in the saturable DNLS is non-trivial, since in
contrast to the cubic DNLS whose nonlinear character is enhanced as the
excitation amplitude increases, the saturable DNLS in fact becomes increasingly
linear as the excitation amplitude increases. We explore the nonlinear dynamics
of this phenomenon by direct numerical simulations
Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr\"odinger Equation with Saturable Nonlinearity
We show that the two-dimensional, nonlinear Schr\"odinger lattice with a
saturable nonlinearity admits periodic and pulse-like exact solutions. We
establish the general formalism for the stability considerations of these
solutions and give examples of stability diagrams. Finally, we show that the
effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero
Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation
Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable
nonlinearity are reported. For finite lattices we find two different
standing-wave-like solutions, and for an infinite lattice we find a localized
soliton-like solution. The existence requirements and stability of these
solutions are discussed, and we find that our solutions are linearly stable in
most cases. We also show that the effective Peierls-Nabarro barrier potential
is nonzero thereby indicating that this discrete model is quite likely
nonintegrable
Effect of thermal noise on the phase locking of a Josephson fluxon oscillator
The influence of thermal noise on fluxon motion in a long Josephson junction is investigated when the motion is phase locked to an external microwave signal. It is demonstrated that the thermal noise can be treated theoretically within the context of a two-dimensional map that models the dynamics of a single fluxon