一类分数阶双分量广义Hirota方程的分数阶孤子解和半群解

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Mathematical Physics Pub Date : 2023-10-16 DOI:10.1155/2023/9996101
Sheng Zhang, Feng Zhu, Bo Xu
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引用次数: 0

摘要

Darboux变换(DT)和广义DT (GDT)在构造可积系统的多孤子解、突变波解和半离散解中发挥了重要作用。本文的主要目的是将DT和GDT推广到一个符合的分数阶双分量广义Hirota (TCGH)方程,以揭示分数阶孤子和半数值解的新动态特性。本文提出了分数阶TCGH方程的分数阶形式,给出了相应的分数阶Lax对,并通过构造分数阶DT和GDT得到了分数阶TCGH方程的分数阶孤子解和半分数阶解。此外,我们发现分数阶的主导作用导致得到的分数阶孤子和半阶解具有新的动态特性,主要包括波峰的一定倾斜以及传播过程中速度和波宽随时间的变化,这是相应的整数阶TCGH方程所不具备的。同时,该研究预测了孤子在分数维介质中的减速传播,为从分数阶优势的角度探索异常波的不对称调节机制提供了可能。
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Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation
The Darboux transformation (DT) and generalized DT (GDT) have played important roles in constructing multisoliton solutions, rogue wave solutions, and semirational solutions of integrable systems. The main purpose of this article is to extend the DT and GDT to a conformable fractional two-component generalized Hirota (TCGH) equation for revealing novel dynamic characteristics of fractional soliton and semirational solutions. As for the main contributions, specifically, we propose a fractional form of the TCGH equation, provide the associated fractional Lax pair, and obtain fractional soliton and semirational solutions of the fractional TCGH equation by constructing its fractional DT and GDT. In addition, we find that the dominant role of fractional order leads to new dynamic characteristics of the obtained fractional soliton and semirational solutions, mainly including a certain degree of tilt of wave crests and the variations in velocities and wave widths over time during propagation, which are not possessed by the corresponding integer-order TCGH equation. Meanwhile, this study predicts the deceleration propagation of solitons in fractional dimensional media and brings the possibility of exploring the asymmetric regulation mechanism of rogue waves from the perspective of fractional-order dominance.
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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