Three wave solution and lump-type solution to a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation with some variable coefficients in inhomogeneous media

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

doi:10.3934/nhm.2025041

Networks and Heterogeneous Media

2025, Volume 20, Issue 3: 955-969. doi: 10.3934/nhm.2025041

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Three wave solution and lump-type solution to a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation with some variable coefficients in inhomogeneous media

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, Shanxi 710049, China

Received: 23 May 2025 Revised: 29 August 2025 Accepted: 02 September 2025 Published: 09 September 2025

This paper focuses on the new (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation with some variable coefficients and derives its new analytical solutions. Based on the (2+1)-dimensional DJKM equation, this equation adds an additional spatial dimension (z) and introduces time-dependent coefficients. Therefore, it is more suitable for describing dynamic wave behaviors in inhomogeneous media. Firstly, by virtue of the Hirota method, we derive the Hirota bilinear form of the equation. Secondly, based on the bilinear form, we present three types of solutions, including the three wave solution and lump-type solution. Finally, by choosing appropriate parameters, we plot some graphs to intuitively display the physical characteristics of these solutions.
- Date-Jimbo-Kashiwara-Miwa equation,
- three wave solution,
- lump-type solution
Citation: Wenjing Yang, Kaili Liu, Bo Tang, Shijie Deng, Fengyun Lv. Three wave solution and lump-type solution to a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation with some variable coefficients in inhomogeneous media[J]. Networks and Heterogeneous Media, 2025, 20(3): 955-969. doi: 10.3934/nhm.2025041

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Abstract

This paper focuses on the new (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation with some variable coefficients and derives its new analytical solutions. Based on the (2+1)-dimensional DJKM equation, this equation adds an additional spatial dimension (z) and introduces time-dependent coefficients. Therefore, it is more suitable for describing dynamic wave behaviors in inhomogeneous media. Firstly, by virtue of the Hirota method, we derive the Hirota bilinear form of the equation. Secondly, based on the bilinear form, we present three types of solutions, including the three wave solution and lump-type solution. Finally, by choosing appropriate parameters, we plot some graphs to intuitively display the physical characteristics of these solutions.

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