Checking out the (3+1)-dimensional Hirota-Wazwaz-El Sherif-El Tantawy bilinear equation modeling oceanic nonlinear wave phenomena

Ocean wave dynamics has emerged as a research focus in Chin. Phys. B. This study investigates the (3+1)-dimensional Hirota-Wazwaz-El Sherif-El Tantawy bilinear equation, a mathematical framework for modeling certain nonlinear wave phenomena in oceans and seas. We combine the equivalent form to that equation, the non-characteristic movable singular manifold, and symbolic computation to deal with the equation. Our findings include an auto-Bäcklund transformation, four families of solitonic solutions, and two families of rational solutions for the equation. All our results hinge on the coefficients in the equation, under the constraints that these coefficients are respectively non-zero. Various choices of these coefficients might aid in exploring certain nonlinear wave phenomena in oceans and seas through our auto-Bäcklund transformation, solitons, and rational solutions.