An ML search for Lax connections recovers known spectral-parameter families in SU(2) PCM and S^2, but the low-loss candidate found for the non-symmetric coset T^{1,1} is a fake Lax connection, not a genuine integrability structure.
Simple identification of fake Lax pairs
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abstract
Two simple ways to identify and explain fake Lax pairs are provided. The two methods are complementary, one involves finding a gauge transformation which can be used to remove the associated nonlinear system's dependent variable(s) from a fake Lax pair. The second method shows that excess degrees of freedom exist in fake Lax pairs. We provide several examples to illustrate both tests. The tests proposed here can be applied to all types of Lax pairs, including scalar or matrix linear problems associated with ordinary or partial difference and/or differential systems.
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Machine-Learning Search for Lax Connections
An ML search for Lax connections recovers known spectral-parameter families in SU(2) PCM and S^2, but the low-loss candidate found for the non-symmetric coset T^{1,1} is a fake Lax connection, not a genuine integrability structure.