REGIONS OF EXISTENCE OF ANALYTICAL SOLUTIONS OF THE (2+1)-DIMENSIONAL SINE-GORDON EQUATION

The sine-Gordon equation is a well-known equation, finding application in a multitude of physical phenomena.In this paper we consider the two-dimensional sine-Gordon equation and its Jacobi elliptic function solutions.We find and illustrate the regions of existence for the solutions, expanding on equivalences found between different solutions.Applying the regions of existence in the setting of band two-dimensional Josephson junctions, a different kind of relation appears between the amplitude of the wave and the width of the junction.Exploring this relation, we give a concrete example of the influence of the wave amplitude on the magnetic field in the junction.