Soliton solutions of Lakshmanan-Porsezian-Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities

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.

This paper secures chirped dark and bright solitons of the perturbed nonlinear Schrödinger equation with parabolic law nonlinearity and self-steepening effect in the nonlinear left-handed metamaterials (NLHMs). We use the ansatz method, sine-cosine, csch function method and the auxiliary equation method to fall out the various soliton solutions. In view of the results obtained, rational, hyperbolic and trigonometric solutions emerge and there are new in CRLH TL. The existence criteria of these solutions are also discussed. Finally, we observed that the use of the auxiliary equation method leads to the abundant and efficient solutions than the other methods.

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.