A new recursion operator for Adlerʼs equation in the Viallet form

Abstract

For Adlerʼs equation in the Viallet form and Yamilovʼs discretisation of the Krichever–Novikov equation we present new recursion and Hamiltonian operators. This new recursion operator and the recursion operator found in [A.V. Mikhailov, et al., Theor. Math. Phys. 167 (2011) 421, arXiv:1004.5346] satisfy the spectral curve associated with the equation.