Stability analysis, optical solitons and complexitons of the two-dimensional complex Ginzburg-Landau equation

In this paper, the two-dimensional complex Ginzburg-Landau equation is investigated, which describes phase transitions in superconductors near their critical temperature in the field of electromagnetic behavior dynamics and in the study of external magnetic fields. We employ the hypothetical method to find the bright soliton, dark soliton and complexitons of the equation. We also find its power series solution with its convergence analysis. Moreover, some constraint conditions are provided which can guarantee the existence of solitons. By use of the Hamiltonian description, we analyze the modulation instability and stable solutions. In order to further understand the dynamic behavior, the graphics analysis is provided of these solutions.