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

Abstract

The paper contains five examples of using cyclic bases of zero-curvature representations in studies of weak and strong Lax pairs, hierarchies of evolution systems, and recursion operators.

arXiv comment18 pages

References in corpus (4)

• Coupled KdV equations of Hirota-Satsuma type
• Integrable Coupled KdV Systems
• A strange recursion operator for a new integrable system of coupled Korteweg - de Vries equations
• Scalar second order evolution equations possessing an irreducible sl${}_2$-valued zero curvature representation

Cited by in corpus (13)

• The short pulse equation is integrable
• On the spectral parameter problem
• Hamiltonian Integrability of Two-Component Short Pulse Equations
• A strange recursion operator for a new integrable system of coupled Korteweg - de Vries equations
• True and fake Lax pairs: how to distinguish them
• Lie algebras responsible for zero-curvature representations of scalar evolution equations
• On Non-Commutative Integrable Burgers Equations
• Enlarged spectral problems and nonintegrability
• On Lie algebras responsible for integrability of (1+1)-dimensional scalar evolution PDEs
• On construction of symmetries and recursion operators from zero-curvature representations and the Darboux-Egoroff system
• A note on Lax pairs of the Sawada-Kotera equation
• Integrability of the Bakirov system: a zero-curvature representation
• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications