Simple identification of fake Lax pairs

2013/11/11 by Samuel Butler, Butler, Samuel, Mike Hay +1 · 1 citation
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.1311.2406

arxiv created 2013/11/11 · arxiv updated 2013/11/12

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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