Solitonic solutions for the reduced Maxwell-Bloch equations via the Darboux transformation and artificial neural network in nonlinear wave dynamics

Abstract

In this article, we explore nonlinear wave dynamics by presenting solitonic solutions for the reduced Maxwell-Bloch equations, a model relevant to both nonlinear optics and Bose-Einstein condensates. First, we derive the Lax pair for the system and apply a Darboux transformation to obtain and analyze the soliton solutions. Then, we introduce a novel approach by integrating the Darboux transformation, a powerful analytical tool, with the Levenberg-Marquardt artificial neural network, a reliable numerical method. This combination enables the identification and validation of soliton solutions, supported by detailed graphical and tabular analyses. The Levenberg-Marquardt artificial neural network effectively demonstrates the uniqueness and convergence of the solutions, with the accuracy of the results validated through comprehensive graphical representations.