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Classification of integrable discrete Klein-Gordon models. (English) Zbl 1221.81092

Summary: The Lie algebraic integrability test is applied to the problem of classification of integrable Klein-Gordon-type equations on quad graphs. The list of equations passing the test is presented, containing several well-known integrable models. A new integrable example is found; its higher symmetry is presented.

MSC:

81R12 Groups and algebras in quantum theory and relations with integrable systems
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
22E70 Applications of Lie groups to the sciences; explicit representations
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