Symmetries in Connection Preserving Deformations

Details Symmetries in Connection Preserving Deformations Symmetries in Connection Preserving Deformations

2011-01-28

arxiv.org/abs/1101.5422v3

SIGMA 7 (2011), 049, 13 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.3842/SIGMA.2011.049

We wish to show that the root lattice of B\"acklund transformations of the $q$-analogue of the third and fourth Painlev\'e equations, which is of type $(A_2+ A_1)^{(1)}$, may be expressed as a quotient of the lattice of connection preserving deformations. Furthermore, we will show various directions in the lattice of connection preserving deformations present equivalent evolution equations under suitable transformations. These transformations correspond to the Dynkin diagram automorphisms.

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