Lax representations and zero-curvature representations by the Kronecker product

DOI10.1007/BF02435889zbMath0946.37032arXivsolv-int/9610008OpenAlexW2065158025MaRDI QIDQ1356581

Fukui Guo, Wen-Xiu Ma

Publication date: 9 July 1997

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9610008

zbMATH Keywords

Kronecker productLax representationszero-curvature representations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (9)

Some soliton hierarchies associated with Lie algebras \(\mathfrak{sp}(4)\) and \(\mathfrak{so}(5)\) ⋮ A new method to construct the integrable coupling system for discrete soliton equation with the Kronecker product ⋮ Component-trace identities for Hamiltonian structures ⋮ KN EQUATIONS HIERARCHY WITH SELF-CONSISTENT SOURCES AND ITS INTEGRABLE COUPLINGS ⋮ INTEGRABLE ASPECTS AND SOLITON-LIKE SOLUTIONS OF AN INHOMOGENEOUS COUPLED HIROTA–MAXWELL–BLOCH SYSTEM IN OPTICAL FIBERS WITH SYMBOLIC COMPUTATION ⋮ A generalization of the Lax equation ⋮ Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations ⋮ A SIMPLE METHOD TO CONSTRUCT INTEGRABLE COUPLING SYSTEM FOR THE MKdV EQUATION HIERARCHY ⋮ COUPLING INTEGRABLE COUPLINGS

Cites Work

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• Lax representation and Kronecker product
• Lectures on Integrable Systems
• Lax pairs galore
• Integrable Models
• Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
• The algebraic structure of zero curvature representations and application to coupled KdV systems
• A hierarchy of coupled Burgers systems possessing a hereditary structure
• The Toda lattice. II. Existence of integrals
• A unified algebraic approach to integral and discrete evolution equations
• A trace identity and its applications to the theory of discrete integrable systems
• An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems

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