Nonlinear Phenomena in Complex Systems, 2020, Vol.23, No.3, pp.338

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2020, Vol.23, No.3, pp.338 - 341

True and Fake Lax Pairs: How to Distinguish Them
Sergei Sakovich

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.

Key words: modified KdV equation, Lax pairs, gauge transformations, invariants

DOI: https://doi.org/10.33581/1561-4085-2020-23-3-338-341

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