Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 43, Issue 23, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/43/23/235201
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The application of the Gardner method for the generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely Backlund transformations and initial conservation laws, follows from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for the generation of symmetries is developed and applied to the discrete Korteweg-de Vries equation. It can also be applied to all the other ABS equations.
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