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The Effect of the Hausdorff Fractal Derivative on Soliton Solutions of Time Space Fractal Sasa-Satsuma Equation with Variable Coefficients
Ibrahim Elkott, M. S. Abdel Latif, I. L. El-Kalla and A. H. Abdel Kader
The aim of this paper is to examine the soliton propagation in a Hausdorff fractal Sasa-Satsuma equation with variable coefficients (HFSSE). A suitable physical system for the HFSSE is an ultrashort optical pulse propagating through a nonlinear fractal-structured metamaterial fiber, where wave dynamics are shaped by third-order dispersion, intensity-dependent nonlinearity, and fractal-induced anomalous memory effects. Applying the unified method, Some new exact soliton solutions of significant importance are obtained for the HFSSE. Under some constraints, some new bright, dark and Rogue wave solitons for the HFSSE are obtained. Finally, the effect of the Hausdorff fractal dimensions on the soliton propagation in the considered Sasa-Satsuma equation is discussed through some figures.
Keywords: Soliton solutions, Sasa-Satsuma equation, Hausdorff fractal derivative, Jacobi elliptic functions