Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube

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• 作者：G. Gubbiotti ; C. Scimiterna ; D. Levi
• 关键词：partial difference equation ; C ; integrability ; Bäcklund transformation ; fake Lax pair
• 刊名：Theoretical and Mathematical Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：189
• 期：1
• 页码：1459-1471
• 全文大小：543 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Applications of Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9333
• 卷排序：189

文摘

We discuss the linearization of a nonautonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized symmetries, which turn out to be nonautonomous and dependent on an arbitrary function of the dependent variables defined at two lattice points. These generalized symmetries are differential–difference equations, which admit peculiar Bäcklund transformations in some cases.