2021/07/15 by Alberto De Sole, De Sole, Alberto, Victor G. Kač +3
Economics, Econometrics and Finance · Mathematics · #37K10 #37K30 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Primary: 35Q53 #Rings and Algebras (math.RA) #Secondary: 35Q51 #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2107.07280
openalex publication_date 2021/07/15 · openalex created_date 2022/11/09 · openalex updated_date 2026/07/28
We define a Lax operator as a monic pseudodifferential operator L(∂) of order N≥ 1, such that the Lax equations \dfrac∂ L(∂)∂ tk=[(L\frac kN(∂))+,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.