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

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

Abstract

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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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

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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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

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