Novel soliton insights into generalized fractional Tzitzéica-type evolution equations using the modified Khater method

Abstract

The primary aim of this paper is to investigate the dynamic behavior of generalized nonlinear fractional Tzitzéica-type equations and to derive optical soliton solutions. To achieve this goal, we employ the modified Khater method, focusing on obtaining solitary wave solutions for generalized fractional Tzitzéica-type (TT) equations. Through this approach, we unveil novel solutions for both Tzitzéica and Tzitzéica–Dodd–Bullough (TDB) equations expressed in terms of fractional derivatives. The significance of employing the modified Khater method lies in its ability to yield a diverse array of soliton solutions. These solutions encompass dark, bright, singular, periodic, kink, singular kink, and combined dark–bright solitons. The derived solutions are visually represented through two-dimensional (2D) and three-dimensional (3D) graphs. Our findings underscore that the proposed method serves as a comprehensive and efficient approach to explore exact solitary wave solutions for generalized fractional TT evolution equations. By employing the modified Khater method, we not only enhance our understanding of the dynamic behavior of these equations, but also provide a versatile tool for obtaining precise soliton solutions in the realm of nonlinear fractional evolution equations.