Novel analytical solutions to the (3 + 1)-dimensional Hirota–Satsuma–Ito-Like equation by using the generalized exponential rational function technique

In the present study, we investigate the (3 + 1)-dimensional Hirota–Satsuma–Ito-Like (HSIL) equation to derive some novel analytical solutions. The HSIL equation arises in various physical phenomena, including fluid dynamics, non-linear optics, and plasma physics. We obtain novel analytical solutions to the HSIL equation by utilizing a relatively new novel analytical technique namely, the generalized exponential rational function (GERF) technique, which offers a systematic approach to solve non-linear partial differential equations. The proposed approach is used to extract various closed form solutions including rational, hyperbolic, trigonometric, and exponential functions solutions. The dynamic behavior of the extracted solutions are presented using 3-D and 2-D plots with help of computational software program like MATHEMATICA. It is observed that some of the obtained solutions are kink and singular periodic type solutions. The derived solutions validate the usefulness and reliability of the suggested method. In addition to providing theoretical insights into the HSIL equation, the discovered solutions have potential applications in a variety of scientific and technical domains, including mathematical physics, wave propagation, and soliton theory. We hold the view that the suggested approach is robust, versatile and capable of generating wave solutions for a diverse area of non-linear evolution equations.