Qualitative analysis and integrable structure of a variable-coefficient noncommutative coupled dispersionless system
In this paper, we investigate a (2+1)-dimensional noncommutative coupled dispersionless (CD) system with variable coefficients. The proposed model extends the classical CD equations by incorporating matrix-valued dependent variables, spatially varying coefficients, and an additional spatial dimension, allowing the study of transverse modulation effects in a noncommutative setting. We show that the resulting system remains integrable by constructing an associated Lax pair and establishing a zero-curvature condition. A Darboux transformation formulated in terms of quasideterminants is developed to generate exact solutions. Using this approach, general quasi-Wronskian expressions for multi-soliton solutions are obtained. Explicit one-soliton and two-soliton solutions are derived and analyzed in both the scalar (commutative) limit and the fully noncommutative case. The influence of variable coefficients and noncommutativity on soliton dynamics is illustrated through representative examples and graphical visualizations. Our results demonstrate that the combined effects of spatial inhomogeneity and noncommutativity lead to richer nonlinear wave structures while preserving integrability.
In this paper, we investigate a (2+1)-dimensional noncommutative coupled dispersionless (CD) system with variable coefficients.
A challenging task in studying geometric function theory is determining the sharp estimates for coefficient-related results that come up in the Taylor series of analytic univalent functions.
The mixed convection heat transfer properties of a square enclosure with a rotating cylinder in the middle are examined in the current work.