Advanced exact solutions to the nano-ionic currents equation through MTs and the soliton equation containing the RLC transmission line

Abstract

In this study, the double (G′/G, 1/G)-expansion method is utilized for illustrating the improved explicit integral solutions for the two of nonlinear evolution equations. To expose the importance and convenience of our assumed method, we herein presume two models, namely the nano-ionic currents equation and the soliton equation. The exact solutions are generated with the aid of our proposed method in such a manner that the solutions involve to the rational, trigonometric, and hyperbolic functions for the first presumed nonlinear equation as well as the trigonometric and hyperbolic functions for the second one with meaningful symbols that promote some unique periodic and solitary solutions. The method used here is an extension of the (G′/G)-expansion method to rediscover all known solutions. We offer 2D and 3D charts of the various recovery solutions to better highlight our findings. Finally, we compared our results with those of earlier solutions. © 2023, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.