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arXiv · 1902.05206

Generating a chain of maps which preserve the same integral as a given map

J. M. Tuwankotta·P. H. van der Kamp·G. R. W. Quispel·K. V. I. Saputra
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Abstract

We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with respect to an integral $H$, to the given system, by exploiting the integral relation, defined by the upshifted version and the original version of $H$. When the numerator of the integral relation is biquadratic or multi-linear, we point out conditions where a dual fails to exists. The procedure is applied to several two-component systems obtained as periodic reductions of 2D lattice equations, including the nonlinear Schrödinger system, the two-component potential Korteweg-De Vries equation, the scalar modified Korteweg-De Vries equation, and a modified Boussinesq system.

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J. M. Tuwankotta, P. H. van der Kamp, G. R. W. Quispel, K. V. I. Saputra. 2019-09-04. Generating a chain of maps which preserve the same integral as a given map. https://doi.org/10.1088/1402-4896%2Fab36f1

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