Exact periodic and explicit solutions of the conformable time fractional Ginzburg Landau equation

摘要

The Ginzburg-Landau (GL) equation is one of the most important nonlinear equation in physics. It is used to model a vast variety of phenomena in physics like nonlinear waves, second order phase transitions, Bose-Einstein condensation, superfluidity, superconductivity, liquid crystals and strings in field theory. In this work, new exact, periodic and explicit solutions of a time fractional GL equation involving conformable fractional derivatives with Kerr law nonlinearity have been found. The Kerr law nonlinearity is due to the non-harmonic motion of electrons under the influence of an applied field. To determine the solution of the model, we have employed a couple of integration algorithms, solitary wave ansatz and expo (-phi(chi)) methods. New periodic and hyperbolic soliton solutions are found as well as the constraint condition for the existence of the solution.