High-order rational-type solutions of the analogous (3+1)-dimensional Hirota-bilinear-like equation

Abstract

In this article, a new dynamical system equation named the (3+1)-dimensional Hirota-bilinear-like equation (HBLE) was constructed. The generalized Hirota bilinear method was applied to obtain this new HBLE in (3+1) dimensions. This new HBLE possesses a similar bilinear form to the original (3+1)-dimensional Hirota bilinear equation, but with additional nonlinear terms. A set of high-order rational solutions is constructed for the given equation, generated from polynomial solutions to the associated generalized bilinear equation. The analyticity conditions of the resulting solutions were investigated and six groups of general solutions were derived. In addition, the shape and surface of the high-order rational function solutions and their dynamic behaviors were studied by utilizing Maple.

Keywords

• hirota bilinear equation
• rational solution
• generalized hirota bilinear method
• hirota bilinear operator
• dynamic behavior