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.
Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube / G. Gubbiotti, C. Scimiterna, D. Levi. - In: THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 0040-5779. - 189:1(2016 Nov 06), pp. 1459-1471. [10.1134/S0040577916100068]
Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube
G. Gubbiotti
;
2016
Abstract
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.File | Dimensione | Formato | |
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