Painlevé analysis and nonlinear wave structures of a variable-coefficient extended KdV equation in $ (3+1) $ dimensions
Year: 2026
Type: article
Abstract: A variable-coefficient Korteweg–de Vries (KdV)-type equation in $ (3+1) $ dimensions is investigated with emphasis on Painlevé integrability and exact nonlinear wave dynamics. Using the Painlevé analysis, the model is shown to possess the Painlevé property under appropriate smoothness and nondegeneracy assumptions on the spatially varying coefficients. A Hirota bilinear representation is subsequently derived, from which an $ N $-soliton solution is constructed. The model admits a variety of exact nonlinear wave structures, including multi-solitons, resonant Y-type waves, fusion and fission waves, X-type solitons, hybrid interaction patterns, and rational lump-type solutions in the admissible parameter regime. The spatially varying coefficients significantly modify soliton trajectories, resonant interaction geometries, and the locations of localized structures, while the exact solutions retain their asymptotic profiles and exhibit shape-preserving interaction patterns. The coexistence of exponential and rational wave structures highlights the richness of the solution space. These results enlarge the class of spatially inhomogeneous nonlinear evolution equations (NLEEs) exhibiting Painlevé–Hirota coherent-wave structures and provide analytical insight into nonlinear wave propagation in spatially inhomogeneous media.
Source: AIMS Mathematics
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W7204158131