Cyclic bases of zero-curvature representations: five illustrations to one concept

DOI10.1023/B:ACAP.0000035589.61486.a7zbMath1062.37081arXivnlin/0212019MaRDI QIDQ702071

Sergei Sakovich

Publication date: 17 January 2005

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0212019

zbMATH Keywords

recursion operatorshierarchiesLax pairs

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Nonlinear evolution equations (47J35)

Related Items (15)

On Lie algebras responsible for integrability of \((1+1)\)-dimensional scalar evolution PDEs ⋮ Lie algebras responsible for zero-curvature representations of scalar evolution equations ⋮ On the (non)removability of spectral parameters in \(\mathbb{Z}_{2}\)-graded zero-curvature representations and its applications ⋮ Unnamed Item ⋮ Enlarged spectral problems and nonintegrability ⋮ Hamiltonian integrability of two-component short pulse equations ⋮ Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube ⋮ A conjecture concerning nonlocal terms of recursion operators ⋮ On Non-Commutative Integrable Burgers Equations ⋮ Equations of pseudo-spherical type (After S. S. Chern and K. Tenenblat) ⋮ On the spectral parameter problem ⋮ Integrability of the Bakirov system: a zero-curvature representation ⋮ On normal forms of irreducible \(\mathfrak{sl}_n\)-valued zero-curvature representations ⋮ On construction of symmetries and recursion operators from zero-curvature representations and the Darboux-Egoroff system ⋮ True and Fake Lax Pairs: How to Distinguish Them

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