Integrability conditions for nonautonomous quad-graph equations |
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| Authors: | R. Sahadevan O.G. Rasin |
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| Affiliation: | a Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai-600 005, Tamil Nadu, India
b Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK |
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| Abstract: | This paper presents a systematic investigation of the integrability conditions for nonautonomous quad-graph maps, using the Lax pair approach, the ultra-local singularity confinement criterion and direct construction of conservation laws. We show that the integrability conditions derived from each of the methods are the one and the same, suggesting that there exists a deep connection between these techniques for partial difference equations. |
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| Keywords: | Quad-graph equations Completely integrable partial difference equations Conservation laws |
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