M.R. Samuelsen

Exact solutions of the saturable discrete nonlinear Schrödinger equation

Exact solutions to a nonlinear Schrodinger 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.

Phase-locking of long annular Josephson junctions coupled to an external rf magnetic field

Abstract Phase-locking of fluxon motion in a long annular Josephson junction coupled to an external magnetic field is demonstrated. applying a simple perturbation method to the perturbedj sine-Gordon system, which models the long Josephson junction. The perturbation result is compared to results of numerical solution of the perturbed sine-Gordon system and good agreement is found.

A simple map describing phase-locking of fluxon oscillations in long Josephson tunnel junctions

Abstract Application of soliton perturbation theory to a Josephson junction fluxon subjected to a microwave field reduces the problem of phase-locking of the fluxon oscillation to the study of a two-dimensional functional map. Phase-locked states correspond to fixed points of the map. The approach captures much of the experimental phenomenology.

Approximate rotationally symmetric solutions to the sine-Gordon equation

Abstract An approximate analytical solution to the two- and three-dimensional sine-Gordon equation, which is an extension of the one soliton solution to the one-dimensional sine-Gordon equation, is shown to give results which agree very well with numerical calculations.

Hysteresis loop induced by rf radiation in Josephson junctions: an analytical approach

Abstract A collective coordinate approach is applied to analyze the effect of an rf signal on the radiation emitted from a long Josephson junction. This system shows a variety of interesting nonlinear phenomena including chaos and hysteresis. Considering the excited localized nonlinear oscillation as an effective breather mode, we derive a nonlinear equation for the collective variable of the breather and analyze the origin of the hysteresis loop. We demonstrate that the hysteresis loop is induced by nonlinearity in the dynamics of an effective ac driven oscillator. Results obtained using this approach are in good agreement with direct numerical simulations.

Non-dissipative perturbations in the sine-gordon system

Abstract Soliton dynamics in simple non-dissipative perturbed sine-Gordon systems are considered. Application conservation laws gives information about asymptotic behaviour of the soliton. Comparison between analytic results and numerical simulations shows good agreement.

Exact and numerical solutions to the perturbed sine-Gordon equation

Abstract We present numerical and analytic solutions to the perturbed sine-Gordon equation, which models long Josephson tunnel junctions. We make comparisons between numerical results and results obtained from perturbational methods. We present unstable, analytic kink solutions to the equation and further a solution, which is an array of kinks, corresponding to a solution, where the current through the junction is larger than the critical current.

An analysis of fluxons in long Josephson junctions

Fluxon propagation in long overlap and inline Josephson junctions is analyzed in the framework of the perturbed sine-Gordon model. The analysis leads to analytical expressions for the zerofield steps, the magnetic field dependence of these, and the line-width of the microwave radiation emitted from the overlap junction. Some of the results are compared to experiments on real junctions.

Subharmonic gap structure and subharmonic Josephson steps

Subharmonic microwave-induced Josephson step structure is often observed in superconducting junctions that exhibit subharmonic gap structure. The two theories, multiparticle tunneling and self-coupling due to an electromagnetic field set up by the ac Josephson current, which have been suggested to explain the subharmonic gap structure are investigated with respect to the possible existence of subharmonic Josephson steps. Also treated is a Ginzburg-Landau calculation of the current-phase relation for Josephson junctions. All three theories give subharmonic Josephson steps with the same microwave-power dependence. The temperature dependence of the subharmonic step structure and the subharmonic gap structure is discussed. It seems the self-coupling is the main cause for both effects in tunnel junctions and for the subharmonic gap structure in Dayem bridges, while the subharmonic step structure in the Dayem bridge seems to be a geometrical effect related to “multiparticle” transfer processes.

Modulation of the breather frequency in the ac-driven sine-Gordon system with loss

Abstract In the sine-Gordon system with loss a breather can be maintained in a steady state if an ac-force of sufficient strength is applied. A small disturbance of this steady state results in a modulation of the breather frequency. The frequency of the modulation is much smaller than the breather frequency and the modulation eventually decays. This modulation frequency is determined by a perturbation method and compared with numerical experiments. Excellent agreement is found.