What question did this study set out to answer?

This work investigates soliton solutions of a time-fractional Konopelchenko-Dubrovsky system focusing on nonlinear wave dynamics.

March 13, 2026

Analytical and Numerical Investigation of Soliton Structures in a Time-Fractional (2+1)-Dimensional Konopelchenko-Dubrovsky System

Puntos clave

This work investigates soliton solutions of a time-fractional Konopelchenko-Dubrovsky system focusing on nonlinear wave dynamics.
Employs a fractional traveling wave transformation to reduce the system to a second-order nonlinear ordinary differential equation.
Utilizes two analytical techniques: the unified method and the Sardar sub-equation method for deriving solutions.
Conducts numerical analyses of soliton characteristics influenced by fractional order and dispersion parameters.
Derives multiple families of soliton solutions including bright, dark, kink-type, singular, and composite waves.
Finds that fractional order significantly affects the amplitude, localization, and structural properties of the solutions.
Demonstrates that fractional dynamics enhance the solution space of the KD system compared to classical integer-order scenarios.

Resumen

In this work, we present a comprehensive analytical and numerical investigation of soliton solutions for a time-fractional Formula: see text-dimensional Konopelchenko–Dubrovsky (KD) system describing multidimensional nonlinear wave propagation with memory effects. The model incorporates a modified Riemann–Liouville time-fractional derivative of order Formula: see text and accounts for nonlinear interaction, longitudinal and transverse dispersion, and coupling mechanisms. The governing system is Formula: see text and by employing a fractional traveling wave transformation, it is reduced to a second-order nonlinear ordinary differential equation describing the wave profile. This reduction preserves the essential balance between nonlinearity, dispersion, and fractional temporal effects, providing a solid foundation for constructing exact solutions. Two complementary analytical techniques, the unified method and the Sardar sub-equation method, are applied to derive multiple families of explicit traveling wave solutions. Several distinct classes of soliton structures, including bright, dark, kink-type, singular, and composite waves, are obtained, illustrating the rich solution space of the fractional KD system. A detailed quantitative analysis is conducted to examine the influence of the fractional order Formula: see text, wave speed, and dispersion parameters on amplitude, localization, and structural behavior of the solutions. Numerical tabulation allows rigorous assessment of how fractional memory effects modify soliton characteristics compared with the classical integer-order case. The results reveal that fractional dynamics significantly enrich the solution structure of the KD system, yielding a broader spectrum of nonlinear wave patterns and demonstrating the robustness, versatility, and mathematical consistency of the proposed analytical framework. This approach offers a reliable foundation for further theoretical and applied investigations of multidimensional fractional nonlinear wave equations arising in geophysics, fluid dynamics, nonlinear optics, and related applied sciences.

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