True and fake Lax pairs: how to distinguish them

Abstract

The gauge-invariant description of zero-curvature representations of evolution equations is applied to the problem of how to distinguish the fake Lax pairs from the true Lax pairs. The main difference between the true Lax pairs and the fake ones is found in the structure of their cyclic bases.

5 pages; v2: sections, discussion, references added

References in corpus (10)

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Cited by in corpus (7)

• Reducibility of zero curvature representations with application to recursion operators
• Simple identification of fake Lax pairs
• Linearizability and fake Lax pair for a consistent around the cube nonlinear non-autonomous quad-graph equation
• Computation of generating symmetries
• Cyclic bases of zero-curvature representations: further examples
• Integrability of one bilinear equation: singularity analysis and dimension
• On continual classes of evolution equations