Soliton Area Theorem for the Cubic Complex Ginzburg-Landau Equation with Drift and Defect in an Electromagnetic Dissipative System - Nonis Airina Mohd Arshad; Ahmad Fateh Mohamad Nor; Nazirah Ramli; Nur Izzati Khairudin (Pandawa Institute, 2026)
This paper presents an approximate ansatz-based solution of the cubic complex Ginzburg-Landau equation (CCGLE) influenced by electromagnetic drift and defect. This study is carried out within the area theorem framework, which describes a relation between soliton energy and duration in dissipative systems. Within this framework, a hyperbolic cosine ansatz is applied to obtain approximate expressions for the soliton energy and duration in the non-integrable dissipative system. From the derivation, the real parameter B in the ansatz is identified as a shape-controlling parameter, which results in three cases known as case I for |B|<1, case II for B > 1, and case III for B = 0. Based on these cases, front stationary solitons are obtained through the balance between the two-parameter family involving non-linearity and dispersion, as well as gain and loss, together with the interaction between drift and defect mechanisms. These interactions allow the system to self-organize into a stable localized structures within the dissipative system. Variations in the parameter B slightly change the soliton profile, especially in terms of width and amplitude. Furthermore, the drift parameter c is varied at c ϵ -0.10, 0.60, 0.95 to investigate the behavior of the area theorem in the CCGLE, where the soliton solutions remain localized during propagation. Overall, the results indicate that the proposed approximate ansatz-based solution is able to describe localized dissipative structures in the non-integrable CCGLE with drift and defect effects.