The Semi-analytical Solutions to the Three Dimensional Complex Ginzburg-Landau Equation

Abstract

For the first time, the solitary wave solutions that can be obtained from the achieved exact solutions by give the appeared parameters definite values to the three dimensional Complex Ginzburg-Landau Equation have been discovered. These solitary wave solutions have been generated in the framework of three impressive semi-analytical algorithms namely the (G'/G)- Algorithm, the Paul-Painlevé Approach Algorithm and the Ricatti-Bernolli-Sub-Ordinary Differential Equation Algorithm. The first two algorithms obey the balance rule while the third one doesn’t obey it. The suggested model has special character in various physics branches, especially in superconductivity, field theory and optics. The generated soliton solutions will give distinctive to the dynamics behaviors of the suggested model that are play principal role in development all related phenomena. New divers types of solitary solutions which weren’t extracted before by anyone have been achieved in forms W, M, shape soliton solutions, bright, dark soliton solutions, combinations between bright and dark soliton solutions, singular soliton solutions, and other rational soliton solutions. The dynamic behaviors simulation operation of the obtained soliton solutions has been designed in 2D, 3D configurators.