Generalized Bigraded Toda Hierarchy

2024/05/30 by Yue Liu, Liu, Yue, Xingjie Yan +5 · 2 citations
Physics and Astronomy · #35Q51 #35Q53 #37K10 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2405.19952

openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bigraded Toda hierarchy L₁^M(n)=L₂^N(n) is generalized to L₁^M(n)=L₂^N(n)+∑_{j∈ \mathbb Z}∑_i=1^mq⁽ⁱ⁾_nΛ^jr⁽ⁱ⁾_n+1, which is the analogue of the famous constrained KP hierarchy L^k= (L^k)_≥0+∑_i=1^mq_i∂^-1r_i. It is known that different bosonizations of fermionic KP hierarchy will give rise to different kinds of integrable hierarchies. Starting from the fermionic form of constrained KP hierarchy, bilinear equation of this generalized bigraded Toda hierarchy (GBTH) are derived by using 2--component boson--fermion correspondence. Next based upon this, the Lax structure of GBTH is obtained. Conversely, we also derive bilinear equation of GBTH from the corresponding Lax structure.

Cited by

• The two--component discrete KP hierarchy
• One reduction of the modified Toda hierarchy

Related

• One reduction of the modified Toda hierarchy
• Lax structure and tau function for large BKP hierarchy
• Generalized fermionic discrete Toda hierarchy
• The constrained KP hierarchy and the bigraded Toda hierarchy of (M,1)-type
• The Extended Toda Hierarchy