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

Wenting Li; Ailing Jiao; Wei Liu; Zhaoying Guo; Wenting Li; Ailing Jiao; Wei Liu; Zhaoying Guo

doi:10.3934/mbe.2023856

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 19360-19371. doi: 10.3934/mbe.2023856

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

1.
Qiongtai Normal University, Haikou 571127, China
2.
School of Mathematics, Heilongjiang University, Harbin 150080, China

Academic Editor: Xiaodi Li

Received: 11 August 2023 Revised: 10 October 2023 Accepted: 13 October 2023 Published: 18 October 2023

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.
- Hirota bilinear equation,
- rational solution,
- generalized Hirota bilinear method,
- Hirota bilinear operator,
- dynamic behavior
Citation: Wenting Li, Ailing Jiao, Wei Liu, Zhaoying Guo. High-order rational-type solutions of the analogous (3+1)-dimensional Hirota-bilinear-like equation[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19360-19371. doi: 10.3934/mbe.2023856

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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.

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