Extending planar two-dimensional structures into the three-dimensional space has become
a general trend in multiple disciplines, including electronics, photonics, plasmonics and …

A magnetic energy functional is derived for an arbitrary curved thin shell on the assumption
that the magnetostatic effects can be reduced to an effective easy-surface anisotropy; it can …

The nonlinear sine-Gordon equation arises in various problems in science and engineering.
In this paper, we propose a numerical scheme to solve the two-dimensional …

During the past few decades, the idea of using differential quadrature methods for numerical
solutions of partial differential equations (PDEs) has received much attention throughout the …

We provide a detailed mathematical explanation of a phenomenon known as the two-
bounce resonance observed in collisions between kink and antikink traveling waves of the …

The method of lines is used to transform the initial/boundary-value problem associated with
the two-dimensional sine-Gordon equation in two space variables into a second-order initial …

In this article, we propose a numerical scheme to solve the one‐dimensional undamped
Sine‐Gordon equation using collocation points and approximating the solution using Thin …

A three-time level finite-difference scheme based on a fourth order in time and second order
in space approximation has been proposed for the numerical solution of the nonlinear two …

We describe a novel effect related to the controlled birth of a single Josephson vortex. In this
phenomenon, the vortex is created in a Josephson transmission line at a T-shaped junction …

We describe new phenomena arising in long and extended Josephson junctions associated
with the two-dimensional character of these junctions. A vortex in such junctions has …