The New Wave Solutions in the Field of Superconductivity

Abstract

In this study, the Landau-Ginzburg-Higgs (LGH) equation, which has the physically important wave solutions, is considered. This equation is discussed via the modified exponential function method (MEFM) to describe superconductivity. Some new solutions are discovered in the form of rational, hyperbolic, and trigonometric functions when compared with the ones taking part in the literature. The functions which are candidates to be the exact solutions of the nonlinear equation are tested by the Mathematica program at the end of the steps of the method and it is observed that they satisfy the LGH equation. Additionally, the 2-D and the 3-D graphs accompanying the density and contour plots are illustrated.