Multi-shock and soliton solutions of the Burgers equation employing Darboux transformation with the help of the Lax pair

IF 1.9 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Pramana Pub Date : 2023-03-27 DOI:10.1007/s12043-023-02534-z

Dipan Saha, Prasanta Chatterjee, Santanu Raut

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引用次数: 2

Abstract

The purpose of this article is to derive a class of multi-soliton solutions of the Burgers equation employing Darboux transformation with the help of the Lax pair. By means of an effective transformation, the Burgers equation is reduced to a suitable form, and accordingly, the Lax pair of the said equation is derived utilising the Ablowitz–Kaup–Newell–Segur (AKNS) approach. Thus, the integrability of the Burgers equation is confirmed. To find an effective solution for the Burgers equation, for the first time, we apply the Darboux transformation through the Lax pair and explore new types of one-soliton solutions and two-soliton solutions of the Burgers equation. These solutions provide some new features of the Burgers equation. To the best of our knowledge, this is the first study in which a parabolic type of structure is found in the Burgers system. Moreover, taking these solutions as the seed solution, higher-order multi-soliton solution can also be generated. Finally, some important three-dimensional plots of the wave solutions are presented to visualise the dynamics of the model.

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在Lax对的帮助下，利用Darboux变换的Burgers方程的多激波和孤子解

本文的目的是在Lax对的帮助下，利用达布变换导出一类Burgers方程的多孤子解。通过有效变换，将Burgers方程简化为合适的形式，并利用ablowitz - kap - newwell - segur (AKNS)方法推导出该方程的Lax对。从而证实了Burgers方程的可积性。为了寻找Burgers方程的有效解，我们首次通过Lax对应用Darboux变换，探索了Burgers方程的单孤子解和双孤子解的新类型。这些解提供了Burgers方程的一些新特征。据我们所知，这是在Burgers系统中首次发现抛物线型结构的研究。并且，将这些解作为种子解，还可以生成高阶多孤子解。最后，给出了波浪解的一些重要的三维图，以使模型的动力学可视化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Pramana 物理-物理：综合

CiteScore

3.60

自引率

7.10%

发文量

206

审稿时长

3 months

期刊介绍： Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.