Fluxon interaction with the finite-size dipole impurity

Abstract

Interaction of the fluxon with the finite size dipole impurity in the long Josephson junction is investigated. The impurity has polarity and will be referred to as a dipole impurity because it also has a direction and, consequently, changes its sign under the space inversion transform x → −x. Such a model is used to describe the inductively coupled to the Josephson transmission line qubit and the misaligned Abrikosov vortex that penetrates into the long Josephson junction. We derive the approximate equations of motion for the fluxon center of mass and its velocity. With the help of these equations we demonstrate that pinning and scattering of the fluxon on the impurity differs significantly from the case of the point impurity which is modelled by the derivative of the Dirac's δ-function.

BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer

“…Note that the residual functions are negative in the domain around the global maximum of U (z), where U > 0, that they are zero (with a cubic dependence on z) where the curves of Fig. 1 change sign, and that they are positive in the domain around their first minimum, where 9) with an exponential corner source (12). The numerical solution U num (red, full line), the zeroth-order U (0) ψ (black, dashed line), the first-order approximant U…”

“…which is an equation for the damped and driven Sine-Gordon model [10], often used to describe the dynamics of Josephson junctions in superconductors [11,12]. Another important application of equation ( 9) is the cubic-quintic Duffing oscillator, which is used to describe damped harmonic motion in a nontrivial potential and has become a paradigm for the study of chaos.…”

“…Traveling wave solution to the nonlinear wave equation(9)with an exponential corner source(12). The numerical solution U num (red, full line), the zeroth-order U(0) ψ (black, dashed line), the first-order approximant U (1) ψ (black, wider spaced dashed line) and the second-order approximant U (2) ψ (black, dot-dashed line, calculated for z < 9) are compared.…”

“…(2) The zeroth-order approximant to the solution of the nonlinear Fisher equation (34) with exponential corner source (12) is…”

Changing the Dynamic Parameters of Localized Breather and Soliton Waves in the Sine-Gordon Model with Extended Impurity, External Force, and Decay in the Autoresonance Mode

“…However, the (1+1)-dimensional models are the most studied. For some applications, it is necessary to account for dissipation and external force in the system (e. g., [1][2][3][10][11][12][13][14]). Parameters of SGE are also often set as functions of coordinates and time [15][16][17][18][19][20].…”