TY - JOUR
T1 - Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method
AU - Rasin, Alexander G.
PY - 2010
Y1 - 2010
N2 - 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 Bäcklund 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.
AB - 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 Bäcklund 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.
UR - http://www.scopus.com/inward/record.url?scp=77952933097&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/43/23/235201
DO - 10.1088/1751-8113/43/23/235201
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AN - SCOPUS:77952933097
SN - 1751-8113
VL - 43
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 23
M1 - 235201
ER -