The soliton solution and periodic lump solution of the (3+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation with variable coefficients

Wenjing Yang; Kaili Liu; Bo Tang; Shijie Deng; Fengyun Lv; Wenjing Yang; Kaili Liu; Bo Tang; Shijie Deng; Fengyun Lv

doi:10.3934/nhm.2026070

Networks and Heterogeneous Media

2026, Volume 21, Issue 5: 1890-1901. doi: 10.3934/nhm.2026070

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The soliton solution and periodic lump solution of the (3+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation with variable coefficients

1.
School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang 441053, China
2.
Hubei Key Laboratory of Power System Design and Test for Electrical Vehicle, Hubei University of Arts and Science, Xiangyang 441053, China
3.
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
4.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Received: 10 July 2026 Revised: 10 August 2026 Accepted: 24 August 2026 Published: 09 September 2026

This paper investigates the soliton solution and periodic lump solution of the $(3+1)$-dimensional generalized Bogoyavlensky–Konopelchenko equation with variable coefficients. First, by introducing specific constraint conditions, a novel bilinear expression for the aforementioned equation is derived. Subsequently, with the aid of symbolic computation, the corresponding soliton and periodic lump solution are successfully constructed. Finally, three-dimensional plots, density plots, and x-axis projection diagrams are presented to analyze the interaction behaviors of the obtained solutions, which provides intuitive visual evidence for the physical characteristics of these solutions.
Citation: Wenjing Yang, Kaili Liu, Bo Tang, Shijie Deng, Fengyun Lv. The soliton solution and periodic lump solution of the (3+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation with variable coefficients[J]. Networks and Heterogeneous Media, 2026, 21(5): 1890-1901. doi: 10.3934/nhm.2026070

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Abstract

This paper investigates the soliton solution and periodic lump solution of the $(3+1)$-dimensional generalized Bogoyavlensky–Konopelchenko equation with variable coefficients. First, by introducing specific constraint conditions, a novel bilinear expression for the aforementioned equation is derived. Subsequently, with the aid of symbolic computation, the corresponding soliton and periodic lump solution are successfully constructed. Finally, three-dimensional plots, density plots, and x-axis projection diagrams are presented to analyze the interaction behaviors of the obtained solutions, which provides intuitive visual evidence for the physical characteristics of these solutions.

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