M-shaped and other exotic solitons generated by cubic-quintic saturable nonlinearities in a nonlinear electrical transmission network with higher-order dispersion effects

This investigation presents the generalized cubic-quintic Guizburg-Landau (GCQGL) equation with higher-order dispersion effects in a nonlinear electrical transmission network. Based on the collective coordinates' theory with a conventional Gaussian Ansatz, the study reveals that the waves which propagate in this medium are exotic solitons such as M-shaped solitons. The investigation presents the stability of the dark soliton subjected to the quintic-phase modulation. Besides, the introduction of the cubic- and quintic-saturable nonlinearities induce the generation of twin narrow solitons, M-shaped soliton and Sasa-Satsuma soliton. Moreover, the introduction of the third-order dispersion (TOD) and the fourth-order dispersion (FOD) provokes the generation of twin large solitons associated to symmetric radiation lobes and twin narrow solitons associated to the damping effect. Some exact field solutions of the GCQGL equation are also illustrated. Moreover, some theoretical frequencies are found where significant results are exposed. In addition, physical conditions associated to the saturation lead to a particular internal perturbation. This internal excitation is measured in detail by the collective coordinates in order to build-up exotic solitons. This technique improves the comprehension of some exotic waves' mechanism of generation in nonlinear electrical transmission network. •Establish the generalized Cubic-quintic Guizburg-Landau (GCQGL) equation with higher order effects.•Physical conditions leading to the generation of some exotic waves when cubic-quintic saturable nonlinearities and high order effects act in the system.•The interaction between complex coefficients and saturation leading to exotic solitons.