Reducibility of zero curvature representations with application to recursion operators

Abstract

We present a criterion of reducibility of a zero curvature representation to a solvable subalgebra, hence to a chain of conservation laws. Namely, we show that reducibility is equivalent to the existence of a section of the generalized Riccati covering. Results are applied to conversion between Guthrie's and Olver's form of recursion operators.

26 pages, uses nath.sty

References in corpus (7)

• Negative order MKdV hierarchy and a new integrable Neumann-like system
• On recursion operators and nonlocal symmetries of evolution equations
• Recursion operator for stationary Nizhnik--Veselov--Novikov equation
• Scalar second order evolution equations possessing an irreducible sl${}_2$-valued zero curvature representation
• True and fake Lax pairs: how to distinguish them
• Time Dependent Recursion Operators and Symmetries
• Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations

Cited by in corpus (16)

• On the spectral parameter problem
• A strange recursion operator demystified
• Simple identification of fake Lax pairs
• Local conservation laws of second-order evolution equations
• Recursion Operators and Nonlocal Symmetries for Integrable rmdKP and rdDym Equations
• Potential Conservation Laws
• Soliton surfaces and generalized symmetries of integrable systems
• Linearizability and fake Lax pair for a consistent around the cube nonlinear non-autonomous quad-graph equation
• Recursion operators for vacuum Einstein equations with symmetries
• On construction of symmetries and recursion operators from zero-curvature representations and the Darboux-Egoroff system
• Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more
• Nonlocal conservation laws of the constant astigmatism equation
• Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation
• On nonlocal symmetries for the Krichever--Novikov equation
• Simplest potential conservation laws of linear evolution equations
• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications