Integrability and complex dynamics of solitons of a generalized perturbed KdV equation with time-dependent variable coefficients and Coriolis effect

Abstract

In this work, the generalized perturbed KdV equation is studied with time-dependent coefficients. The integrability of the proposed equation is demonstrated with the help of Painlevé test ($P$-test) criteria. It is verified that the considered equation possess analytical solutions in the form of solitons as it does not have movable singularity, which is verified via $P$-test. The N-soliton with time dependent coefficients is achieved via Hirota direct method. First, second and third-order soliton solutions are derived with suitable auxiliary functions. Moreover, hybrid lump solutions are attained via Hirota bilinear form. Detailed graphical presentations, including 3D visualizations, illustrate the dynamics of the soliton solutions, emphasizing the influence of the time-dependent Coriolis effect on soliton behavior. These results advance the understanding of the time-dependent integrable systems and offer significant insights into the dynamics affected by variable external factors, contributing to broader applications in fluid dynamics and nonlinear wave propagation.