Some Important Points of the Josephson Effect via Two Superconductors in Complex Bases

Abstract

In this paper, we study the extraction of some analytical solutions to the nonlinear perturbed sine-Gordon equation with the long Josephson junction properties. The model studied was formed to observe the long Josephson junction properties separated by two superconductors. Moreover, it is also used to explain the Josephson effect arising in the highly nonlinear nature of the Josephson junctions. This provides the shunt inductances to realize a Josephson left-handed transmission line. A powerful scheme is used to extract the complex function solutions. These complex results are used to explain deeper properties of Josephson effects in the frame of impedance. Various simulations of solutions obtained in this paper are also reported.

Keywords

• nonlinear perturbed sine-Gordon equation
• Bernoulli sub-equation function method
• complex travelling wave solutions
• singular solitons