Optical Soliton Solutions for the Conformable Nonlinear Hybrid-Lattice Equation Using the Generalized Kudryashov Method
Keywords:
Hybrid-Lattice Equation, Conformable Calculus, Generalized Kudryashov Method, Optical Solitons, Discrete Systems, Singularity AnalysisAbstract
In this work, we investigate the propagation of nonlinear waves in a discrete semi-infinite chain modeled by the conformable Hybrid-Lattice equation. By employing the continuum limit approximation, we transform the governing Differential-Difference Equation (DDE) into a nonlinear partial differential equation with fractional temporal evolution. We propose the application of the Generalized Kudryashov Method (GKM), a robust analytical technique that constructs solutions using exponential rational functions. This approach yields new exact solutions, including topological kink solitons and singular blow-up waves, which are essential for understanding energy transport and instability in nonlinear lattices. The impact of the fractional order α and the auxiliary base parameter A on the wave velocity and steepness is analyzed through comprehensive numerical simulations. The results demonstrate the efficiency of the GKM in solving fractional nonlinear evolution equations.
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Copyright (c) 2026 Aysel Ramazanova, Hazal Yüksekkaya, Nasir Ali, Davron Aslonqulovich Juraev (Author)
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