We define a Lax operator as a monic pseudodifferential operator L(∂) of order N ≥ 1, such that the Lax equations ∂L(∂)∂tk=[(L_k^N(∂))_+,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.
On Lax operators / De Sole, A.; Kac, V. G.; Valeri, D.. - In: JAPANESE JOURNAL OF MATHEMATICS. NEW SERIES. - ISSN 0289-2316. - 17:1(2022), pp. 63-116. [10.1007/s11537-021-2134-1]
On Lax operators
De Sole A.;Valeri D.
2022
Abstract
We define a Lax operator as a monic pseudodifferential operator L(∂) of order N ≥ 1, such that the Lax equations ∂L(∂)∂tk=[(L_k^N(∂))_+,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.| File | Dimensione | Formato | |
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