Abstract
In this study, the Landau-Ginzburg-Higgs (LGH) equation which has the physically important wave solutions is considered. This equation is discussed via 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 candidate to be the exact solutions of the nonlinear equation are tested by 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.
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