New shape of the chirped bright, dark optical solitons and complex solutions for (2+1)-dimensional Ginzburg-Landau equation and modulation instability analysis - Houwe, A.; İnç, Mustafa; Baleanu, D.; Rezazadeh, H.; Doka, S. Y. (Soc Mexicana Fisica, 2021)
The investigation of the Ginzburg-Landau equation (GLE) has been done to fin out and investigate new chirped bright, dark periodic and singular function solutions. For this purpose, we have used the traveling wave hypothesis and the chirp component. From there it was pointed out the constraint relation to the different arbitrary parameters of the GLE. Thereafter, we have employed the improved sub-ODE method to handle the nonlinear ordinary differential equation (NODE). In the paper, the virtue of the used analytical method has been highlighted via new chirped solitary waves. Besides, to emphasize the confrontation between the nonlinearity and dispersion terms, we have investigated the steady state of the newly obtained results. It has been obtained the Modulation instability (MI) gain spectra under the effect of the power incident and the transverse wave number. In our knowledge, these results are new compared to Refs. [28-34], and are going to be helpful to explain physical phenomena.
Keywords: Chirped bright and dark; Complex solutions; (2+1)-Ginzburg-Landau equation; modulation instability