Purpose

The purpose of this paper is to investigate a variety of Painlevé integrable equations derived from a Hamiltonian equation.

Design/methodology/approach

The newly developed Painlevé integrable equations have been handled by using Hirota’s direct method. The authors obtain multiple soliton solutions and other kinds of solutions for these six models.

Findings

The developed Hamiltonian models exhibit complete integrability in analogy with the original equation.

Research limitations/implications

The present study is to address these two main motivations: the study of the integrability features and solitons and other useful solutions for the developed equations.

Practical implications

The work introduces six Painlevé-integrable equations developed from a Hamiltonian model.

Social implications

The work presents useful algorithms for constructing new integrable equations and for handling these equations.

Originality/value

The paper presents an original work with newly developed integrable equations and shows useful findings.

中文翻译：

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哈密​​顿方程产生各种 Painlevé 可积方程：不同物理结构的解

目的

本文的目的是研究从哈密顿方程导出的各种 Painlevé 可积方程。

设计/方法论/途径

新开发的 Painlevé 可积方程已使用 Hirota 直接法进行处理。作者获得了这六个模型的多个孤子解和其他类型的解。

发现

开发的哈密顿模型表现出与原始方程类似的完全可积性。

研究局限性/影响

本研究旨在解决这两个主要动机：研究可积特征和孤子以及所开发方程的其他有用的解决方案。

实际影响

这项工作介绍了从哈密顿模型开发的六个 Painlevé 可积方程。

社会影响

这项工作提出了构建新的可积方程和处理这些方程的有用算法。

原创性/价值

该论文提出了新开发的可积方程的原创性工作，并展示了有用的发现。