Wave propagation of the perturbed nonlinear Schrödingers equation in the nonlinear left-handed transmission lines

In this paper, we studies chirped solitary waves in two-Core optical fibers with coupling-coefficient dispersion and intermodal dispersion. To construct chirp soliton, the couple of nonlinear Schrödinger equation which describing the pulses propagation along the two-core fiber have been reduced to one equivalent equation. By adopting the traveling-waves hypothesis, the exact analytical solutions of the GNSE were obtained by using three relevant mathematical methods namely the auxiliary equation method, the modified auxiliary equation method and the Sine-Gordon expansion approach. Lastly, the behavior of the chirped like-soliton solutions were discussed and some contours of the plot evolution of the bright and dark solitons are obtained.

Abstract The optical solitons in Bragg gratings fibers for perturbed NLSE having cubic-quartic dispersive reflectivity with parabolic-nonlocal combo law of refractive index are studied. The extended auxiliary equation method and the addendum to Kudryashov's method are introduced. The existence criteria for such solitons are indicated.

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.