Lenard scheme for multi-Hamiltonian systems

Lenard scheme is used to generate infinitely many symmetries and conservation laws for multi-Hamiltonian systems. In this talk, I'll formulate the easily verified conditions for compatible weakly nonlocal Hamiltonian and symplectic operators to generate local hierarchies, and sketch the proof in the context of variational complex. I'll give examples for both continuous and discrete integrable systems including two-dimensional periodic Volterra chain and the discrete Adler's equation.