Equivalence of formulations of the MKP hierarchy and its polynomial\n tau-functions

2018/01/09 by Victor G. Kač, Kac, Victor, Johan van de Leur +1 · 3 citations
Engineering · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Optical Network Technologies #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1801.02845

openalex publication_date 2018/01/09 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We give 4 formulations of the Modified KP hierarchy and show that they are\nequivalent. We also discuss the reductions of the MKP hierarchy to the modified\nn-KdV hierarchies. As a byproduct, we find an astonishingly simple explicit\ndescription of all polynomial tau-functions of the KP, the MKP and the n-KdV\nhierarchies, and (implicitly) also for the modified n-KdV hierarchy.\n

Cited by

• Open Hurwitz numbers and the mKP hierarchy
• The two--component discrete KP hierarchy
• One reduction of the modified Toda hierarchy

Related

• Polynomial tau-functions of the n-th Sawada-Kotera hierarchy
• Tau-function of the multi-component CKP hierarchy
• Polynomial tau-functions for the multi-component KP hierarchy
• Formal solution to the KP hierarchy
• From the Adler--Moser polynomials to the polynomial tau functions of KdV