New algorithm for deriving rational form solutions in the generalized Date-Jimbo-Kashiwara-Miwa model

This paper introduces, for the first time, the application of rational form solutions involving sine-cosine and sinh-cosh functions to address a nonlinear model emerging in the realm of plasma physics. The model under consideration is derived from the KP hierarchy and is denoted as the Date-Jimbo-Kashiwara-Miwa equation. In this study, the proposed model is extended to incorporate arbitrary coefficients, encompassing both nonlinearity and dispersion factors. The solutions obtained are presented through 2D and 3D plots, revealing three distinct types of solitary wave propagation: moving singular-periodic, kink, and singular solutions. These solutions, as reported in this work, have the potential for broader applications, including optics and quantum physics.