Theoretical analysis for miscellaneous soliton waves in metamaterials model by modification of analytical solutions

In this article, the new exact solitary wave solutions for the generalized nonlinear Schrodinger equation with parabolic nonlinear (NL) law employing the improved tanh(Gamma(pi))-coth(Gamma(pi)) function technique and the combined tan(Gamma(pi))-cot(Gamma(pi)) function technique are obtained. The offered techniques are novel and also for the first time in this study are used. Different collections of hyperbolic and trigonometric function solutions acquired rely on a map between the considered equation and an auxiliary ODE. The several hyperbolic and trigonometric forms of solutions based on diverse restrictions between parameters involved in equations and integration constants that appear in the solution are obtained. A few significant ones among the reported solutions are pictured to perceive the physical utility and peculiarity of the considered model utilizing mathematical software. The main subject of this work is that one can visualize and update the knowledge to overcome the most common techniques and defeat to solve the ODEs and PDEs. The concluded solutions are demonstrated where are valid by using Maple software and also found those are correct. The proposed methodology for solving the metamaterilas model are designed where is effectual, unpretentious, expedient, and manageable. Finally, the existence of the obtained solutions for some conditions is also analyzed.

Automated summary

This article investigates the new exact solitary wave solutions for the generalized nonlinear Schrodinger equation with parabolic nonlinear law. These solutions are obtained using the improved function technique. Different forms of solutions are obtained based on the map between the considered equation and an auxiliary ODE.