A SOLITON HIERARCHY FROM THE LEVI SPECTRAL PROBLEM AND ITS TWO INTEGRABLE COUPLINGS, HAMILTONIAN STRUCTURE

DOI10.1142/S0217984909018953zbMath1196.37113OpenAlexW2050690198MaRDI QIDQ3629912

Yan Li, Yongqing Zhang

Publication date: 2 June 2009

Published in: Modern Physics Letters B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0217984909018953

zbMATH Keywords

Lie algebraHamiltonian structuresoliton equationLevi spectral problem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Cites Work

• Two unified formulae
• Invertible linear transformations and the Lie algebras
• Integrable theory of the perturbation equations.
• A higher-dimensional Lie algebra and its decomposed subalgebras
• Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Enlarging spectral problems to construct integrable couplings of soliton equations
• New integrable couplings and Hamiltonian structure of the KN hierarchy and the DLW hierarchy
• A hierarchy of coupled Korteweg-de Vries equations and the normalisation conditions of the Hilbert-Riemann problem
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
• A simple model of the integrable Hamiltonian equation
• Korteweg-deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
• The quadratic-form identity for constructing the Hamiltonian structure of integrable systems

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