Purpose

The purpose of this paper is to introduce a variety of new completely integrable Calogero–Bogoyavlenskii–Schiff (CBS) equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for each of the developed models.

Design/methodology/approach

The newly developed models with time-dependent coefficients have been handled by using the simplified Hirota’s method. Moreover, multiple complex soliton solutions are derived by using complex Hirota’s criteria.

Findings

The developed models exhibit complete integrability, for specific determined functions, by investigating the compatibility conditions for each model.

Research limitations/implications

The paper presents an efficient algorithm for handling integrable equations with analytic time-dependent coefficients.

Practical implications

The work presents new integrable equations with a variety of time-dependent coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.

Social implications

This study presents useful algorithms for finding and studying integrable equations with time-dependent coefficients.

Originality/value

The paper gives new integrable CBS equations which appear in propagation of waves and provide a variety of multiple real and complex soliton solutions.

中文翻译：

---

具有时间相关系数的多种完全可积分的Calogero–Bogoyavlenskii–Schiff方程

目的

本文的目的是介绍具有时变系数的各种新的完全可积分的Calogero–Bogoyavlenskii–Schiff（CBS）方程。作者为每个开发的模型获得了多个孤子解决方案和多个复杂孤子解决方案。

设计/方法/方法

通过使用简化的Hirota方法处理了具有随时间变化的系数的新开发的模型。此外，通过使用复杂的Hirota准则可以导出多个复杂的孤子解。

发现

通过研究每种模型的兼容性条件，已开发的模型对于特定的确定功能具有完全的可集成性。

研究局限/意义

本文提出了一种有效的算法，用于处理具有解析时间相关系数的可积方程。

实际影响

这项工作提出了具有各种时间相关系数的新可积方程。作者表明，具有随时间变化的系数的可积方程给出了实和复杂的孤子解。

社会影响

这项研究提出了有用的算法，用于查找和研究具有时间相关系数的可积分方程。

创意/价值

本文给出了在波传播中出现的新的可积分CBS方程，并提供了多种多重的实和复孤子解。