Lax Formulation of 3-Component KP Hierarchy by Shiota Construction

It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 35; no. 5
Main Authors Cui, Tongtong, Wang, Jinbiao, Cao, Wenqi, Cheng, Jipeng
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2025
Springer Nature B.V
Subjects
Analysis
Classical Mechanics
Differential equations
Economic Theory/Quantitative Economics/Mathematical Methods
Finite differences
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Theoretical
Tau function
3-Component KP
Lax equation
35Q53
35Q51
37K10
Bilinear equation
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Summary:It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators Λ 1 and Λ 2 , where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases.
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ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-025-10190-3