Purpose

This paper aims to explore new variable separation solutions for a new generalized (3 + 1)-dimensional breaking soliton equation, construct novel nonlinear excitations and discuss their dynamical behaviors that may exist in many realms such as fluid dynamics, optics and telecommunication.

Design/methodology/approach

By means of the multilinear variable separation approach, variable separation solutions for the new generalized (3 + 1)-dimensional breaking soliton equation are derived with arbitrary low dimensional functions with respect to {y, z, t}. The asymptotic analysis is presented to represent generally the evolutions of rogue waves.

Findings

Fixing several types of explicit expressions of the arbitrary function in the potential field U, various novel nonlinear wave excitations are fabricated, such as hybrid waves of kinks and line solitons with different structures and other interesting characteristics, as well as interacting waves between rogue waves, kinks, line solitons with translation and rotation.

Research limitations/implications

The paper presents that a variable separation solution with an arbitrary function of three independent variables has great potential to describe localized waves.

Practical implications

The roles of parameters in the chosen functions are ascertained in this study, according to which, one can understand the amplitude, shape, background and other characteristics of the localized waves.

Social implications

The work provides novel localized waves that might be used to explain some nonlinear phenomena in fluids, plasma, optics and so on.

Originality/value

The study proposes a new generalized (3 + 1)-dimensional breaking soliton equation and derives its nonlinear variable separation solutions. It is demonstrated that a variable separation solution with an arbitrary function of three independent variables provides a treasure-house of nonlinear waves.

中文翻译：

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广义 (3+1) 维破缺孤子方程的新颖局域波和动力学分析

 目的

本文旨在探索新的广义（3 + 1）维破缺孤子方程的新变量分离解，构造新的非线性激励并讨论它们可能存在于流体动力学、光学和电信等许多领域的动力学行为。

设计/方法论/途径

通过多线性变量分离方法，利用关于{ y ， z ， t }的任意低维函数导出了新的广义(3+1)维破缺孤子方程的变量分离解。渐进分析通常代表了异常波的演化。

 发现

固定势场 U 中任意函数的几种显式表达式，构造出各种新颖的非线性波激励，例如具有不同结构和其他有趣特征的扭结和线孤子的混合波，以及流氓波之间的相互作用波，扭结，具有平移和旋转的线孤子。

研究局限性/影响

该论文提出，具有三个自变量的任意函数的变量分离解具有描述局域波的巨大潜力。

 实际意义

本研究确定了所选函数中参数的作用，据此可以了解局域波的振幅、形状、背景等特征。

 社会影响

这项工作提供了新颖的局域波，可用于解释流体、等离子体、光学等中的一些非线性现象。

 原创性/价值

研究提出了一种新的广义(3+1)维破缺孤子方程并推导了其非线性变量分离解。事实证明，具有三个自变量的任意函数的变量分离解提供了非线性波的宝库。