修正的科特维格-德弗里斯-本杰明-奥诺方程的大时间渐近线

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-07 DOI:10.1016/j.na.2024.113604

Nakao Hayashi , Jesus A. Mendez-Navarro , Pavel I. Naumkin

引用次数: 0

摘要

我们研究修正的 Korteweg-de Vries-Benjamin-Ono 方程 ∂tu+a2H∂x2u-b3∂x3u=∂xu3,t>0,x∈R,u0,x=u0x,x∈R 的 Cauchy 问题解的大时间渐近性，其中 a,b>0, Hj=1πp.v.∫Rϕyx-ydy 是希尔伯特变换。我们开发了因式分解技术来获得解的尖锐时间衰减估计值，并证明了修正散射。

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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Large time asymptotics for the modified Korteweg–de Vries-Benjamin–Ono equation

We study the large time asymptotics of solutions to the Cauchy problem for the modified Korteweg–de Vries-Benjamin–Ono equation $(\begin{matrix} \partial_{t} u + \frac{a}{2} H \partial_{x}^{2} u - \frac{b}{3} \partial_{x}^{3} u = \partial_{x} (u^{3}), t > 0, x \in R, u (0, x) = u_{0} (x), x \in R, \end{matrix})$ where $a, b > 0,$ $H ϕ = \frac{1}{π}$ p.v. $\int_{R} \frac{ϕ (y)}{x - y} d y$ is the Hilbert transform. We develop the factorization technique to obtain the sharp time decay estimate for solutions and to prove the modified scattering.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.