Numerical simulations of chaotic structures and soliton interactions in the (3+1)-dimensional date–Jimbo–Kashiwara–Miwa equation

This study aims to investigate an in-depth analysis of the (3+1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation describing the propagation of nonlinear dispersive waves in inhomogeneous media. By using the Hirota bilinear method, we derive an extensive range of exact solutions, the resonant Y-type and X-type soliton waves and hybrid resonant solitons. Moreover, we determine the lump-periodic, lump-rogue and breather wave interactions using a specific ansatz function method. These solutions are significant in nonlinear wave phenomena showing complex wave interactions and the balance between coherence and dispersion. For validity and reliability of reported results, we display them through 3D, 2D, density and contour plots under suitable parameter values and resonant conditions. Similarly, we investigate the perturbed dynamical system employing chaos detection tools such as phase portraits, power spectra and return maps, which confirm its chaotic behavior. These findings are significant, as they underscore the nonlinear dynamics inherent in models of mathematical physics, fluid dynamics, optics and engineering.