Purpose

This paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t. The new equation models both right- and left-going waves in a like manner to the Boussinesq equation.

Design/methodology/approach

This formally uses the simplified Hirota’s method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space.

Findings

This paper confirms the complete integrability of the newly developed (3 + 1)-dimensional model in the Painevé sense.

Research limitations/implications

This paper addresses the integrability features of this model via using the Painlevé analysis.

Practical implications

This paper presents a variety of lump solutions via using a variety of numerical values of the included parameters.

Social implications

This work formally furnishes useful algorithms for extending integrable equations and for the determination of lump solutions.

Originality/value

To the best of the author’s knowledge, this paper introduces an original work with newly developed integrable equation and shows useful findings of solitons and lump solutions.

中文翻译：

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新的（3+1）维可积四阶非线性方程：团块和多孤子解

目的

本文旨在介绍一个新的（3+1）维四阶可积方程，其特征是在时间t上的二阶导数。新方程以与 Boussinesq 方程类似的方式模拟右行波和左行波。

设计/方法/方法

这正式使用简化的 Hirota 方法和块方案来确定多个孤子解和块解，它们在空间的各个方向上合理地定位。

发现

本文证实了新开发的 (3+1) 维模型在 Paineve 意义上的完全可积性。

研究限制/影响

本文通过使用 Painlevé 分析解决了该模型的可积性特征。

实际影响

本文通过使用包含参数的各种数值提出了各种集中解。

社会影响

这项工作正式提供了用于扩展可积方程和确定块解的有用算法。

原创性/价值

据作者所知，本文介绍了新开发的可积方程的原创作品，并展示了孤子和块解的有用发现。