On Lax operators

De Sole, A., Kac, V. G. and Valeri, D. (2022) On Lax operators. Japanese Journal of Mathematics, 17(1), pp. 63-116. (doi: 10.1007/s11537-021-2134-1)

Abstract

We define a Lax operator as a monic pseudodifferential operator L(∂) of order N ≥ 1, such that the Lax equations ∂L(∂)∂tk=[(LkN(∂))+,L(∂)] 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Valeri, Dr Daniele
• Authors: De Sole, A., Kac, V. G., and Valeri, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Japanese Journal of Mathematics
• Publisher: Springer
• ISSN: 0289-2316
• ISSN (Online): 1861-3624
• Published Online: 10 December 2021
• Copyright Holders: Copyright © 2021 The Mathematical Society of Japan and Springer Japan KK, part of Springer Nature
• First Published: First published in Japanese Journal of Mathematics 17(1): 63-116
• Publisher Policy: Reproduced in accordance with the publisher copyright policy