TY - JOUR T1 - Fluxon Centering in Josephson Junctions with Exponentially Varying Width JO - East Asian Journal on Applied Mathematics VL - 3 SP - 204 EP - 213 PY - 2018 DA - 2018/02 SN - 2 DO - http://doi.org/10.4208/eajam.230512.010712a UR - https://global-sci.org/intro/article_detail/eajam/10873.html KW - Fluxon, stability, bifurcation, critical curve, centering magnetic field, centering current. AB -

Nonlinear eigenvalue problems for fluxons in long Josephson junctions with exponentially varying width are treated. Appropriate algorithms are created and realized numerically. The results obtained concern the stability of the fluxons, the centering both magnetic field and current for the magnetic flux quanta in the Josephson junction as well as the ascertaining of the impact of the geometric and physical parameters on these quantities. Each static solution of the nonlinear boundary-value problem is identified as stable or unstable in dependence on the eigenvalues of associated Sturm-Liouville problem. The above compound problem is linearized and solved by using of the reliable Continuous analogue of Newton method.