Super integrable hierarchies associated with spl(2, 1) and Darboux transformations

DOI10.1063/1.5018031zbMath1393.37075OpenAlexW2776125977MaRDI QIDQ4600226

Liangyun Chen, Baiying He

Publication date: 8 January 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.5018031

zbMATH Keywords

Lie superalgebrasoliton hierarchiessuper-Hamiltonian structure

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of Lie algebras and superalgebras to integrable systems (17B80) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Cites Work

• Two \((2+1)\)-dimensional hierarchies of evolution equations and their Hamiltonian structures
• Darboux transformations for a Lax integrable system in \(2n\) dimensions
• One-parameter homogeneous differential realization and boson-fermion realization of the SPL(2,1) superalgebra
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Super Jaulent-Miodek hierarchy and its super Hamiltonian structure, conservation laws and its self-consistent sources
• A few super-integrable hierarchies and some reductions, super-Hamiltonian structures
• Representation theory of \(\mathfrak{sl}(2|1)\)
• Three New Integrable Hierarchies of Equations
• A Super Extension of Kaup—Newell Hierarchy
• A supertrace identity and its applications to superintegrable systems
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A trace identity and its application to integrable systems of 1 + 2 dimensions
• Induced Lie Algebras of a Six-Dimensional Matrix Lie Algebra
• Super-KN Hierarchy and Its Super-Hamiltonian Structure