关于Lax算子

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-12-10 DOI:10.1007/s11537-021-2134-1

Alberto De Sole, Victor G. Kac, Daniele Valeri

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引用次数: 3

摘要

我们将Lax算子定义为N≥1阶的单伪微分算子L(∂)，使得Lax方程\(\frac{\partial L(\partial)}{\partial t_k}=[(L^\frac{k}{N}(\partial))_+,L(\partial)]\)对于无穷多个正整数k是一致且非零的。方程的一致性意味着它的流是由演化向量场定义的。在本文中，我们证明了KP和n阶KdV的传统理论对任意标量Lax算子成立。

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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On Lax operators

We define a Lax operator as a monic pseudodifferential operator L(∂) of order N ≥ 1, such that the Lax equations \(\frac{\partial L(\partial)}{\partial t_k}=[(L^\frac{k}{N}(\partial))_+,L(\partial)]\) are consistent and non-zero for infinitely many positive integers k. Consistency of an equation means that its flow is defined by an evolutionary vector field. In the present paper we demonstrate that the traditional theory of the KP and the N-th KdV hierarchies holds for arbitrary scalar Lax operators.

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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.