Study of the two‐dimensional sine‐Gordon equation arising in Josephson junctions using meshless finite point method

In this paper, the finite point method is discussed for solving the initial-boundary value problem associated with the sine-Gordon equation in two-dimensional domains arising in the Josephson junctions problem. The resulting nonlinear system is solved using an appropriate predictor-corrector scheme. The proposed scheme is simple and efficient. The collisional properties for cases involving the most known from the bibliography, line, and ring solitons are studied in numerical results. Also the birth of a single Josephson vortex in a Josephson transmission line at a T-shaped junction is studied.