具有时滞的Korteweg-de Vries方程中的周期波和孤立波

IF 1.3 3区数学 Q1 MATHEMATICS

Proceedings of the Royal Society of Edinburgh Section A-Mathematics Pub Date : 2023-09-07 DOI:10.1017/prm.2023.88

Qi Qiao, Shuling Yan, Xiang Zhang

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引用次数: 0

摘要

对于一类具有分布时滞的扰动广义Korteweg-de Vries方程，利用几何奇异摄动理论和Melnikov方法证明了周期波和孤立波的存在性。进一步得到周期波速度相对于无摄动系统总能量的单调性和有界性。最后，我们建立了波速与波长之间的关系。

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Periodic and solitary waves in a Korteweg–de Vries equation with delay

For a perturbed generalized Korteweg–de Vries equation with a distributed delay, we prove the existence of both periodic and solitary waves by using the geometric singular perturbation theory and the Melnikov method. We further obtain monotonicity and boundedness of the speed of the periodic wave with respect to the total energy of the unperturbed system. Finally, we establish a relation between the wave speed and the wavelength.

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来源期刊

Proceedings of the Royal Society of Edinburgh Section A-Mathematics 数学-数学

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.