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This study explores the dynamics of a Formula: see text-dimensional extended Kairat-X equation, revealing its connections to differential geometry of curves and equivalence principles. Using the Hirota bilinear method and linear superposition principle (LSP), we derived lump-periodic solutions, higher-order solitons with bifurcations, resonant multi-soliton waves, and positive complexiton solutions. To highlight the significance of these results, we present 3D, density and contour plots for specific parameter values. Also, we analyzed the modulation instability (MI) by determining the stability region and gain spectrum. This novel work offers valuable insights into the integrable model introduced by Wazwaz, and provides algorithms for investigating newly developed systems related to plasma physics, optical communications, marine dynamics, and the geometry of curves.
Rafiq et al. (Mon,) studied this question.