Solitonic Solutions for the Coupled Burgers Equation in Space-TimeUsing Composite Derivatives
DOI:
https://doi.org/10.22105/kmisj.v2i1.124Keywords:
Coupled Burgers’ equation, Composite CN-derivative, Exact soliton solutions, Integral traveling wave variableAbstract
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.
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