Solitonic Solutions for the Coupled BurgersEquation in Space-Time using CompositeDerivatives CN

Abstract

In this article, we investigate the coupled Burgers equation in spacetime
governed by the local composite derivative CN. By defining a generalized
traveling variable transformation, we reduce the coupled system
of partial differential equations to integrable ordinary differential equations.
Using a hyperbolic ansatz, we derive soliton solutions and evaluate
them for three representative kernel classes: potential, exponential, and
Mittag-Leffler. We also show that the conformable derivative formulation
represents only a restricted monomial subset of our generalized integral
framework. Numerical simulations and contour visualizations illustrate
how the choice of kernel distorts the wavefront geometry and phase propagation in nonhomogeneous media.