Linear Stability Analysis of Solitons Governed by the 2D Complex Cubic-Quintic Ginzburg-Landau Equation

. We used the singular value decomposition to construct a low-dimensional model that qualitatively describes the behavior and dynamics of optical solitons governed by the complex cubic-quintic Ginzburg-Landau equation in two spatial dimensions. With this model, it was found that a single soliton destabilizes and transitions into a double-soliton configuration through an intermediate periodic phase as the gain increases. Linear stability analysis then revealed that a Hopf bifurcation occurs at several critical gain values corresponding to the destabilization of the single and double solitons.