A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields

To obtain coverings of [ref], we consider the following scheme applied before, for example, in [ref] , cf. also [ref] : 1) The nonlocal variable $w$ given by the Lax pair [ref] is expanded in a formal series in the spectral parameter $λ$, resp. $μ$: [equation] 2) By substituting this expansion into the Lax pair [ref] and eliminating the parameter $λ$, resp. $μ$, we get an infinite series of nonlocal quantities $w_i$, $i ∈Z$. 3) To achieve the proper definition of nonlocal variables $w_i$, we consider two reductions of the series $w_i$: (a) the negative reduction $w_i=0$ for $i>0$ and (b) the positive reduction $w_i=0$ for $i<0$. 4) In this way, we arrive at the following three inequivalent infinite-dimensional coverings $τ^q$, $τ^m$ and $τ^r$ (given in the form of Lax pairs) with the nonlocal variables $q_α,m_α,r_β$ respectively, where: [equation]

On recursion operators for full-fledged nonlocal symmetries of the reduced quasi-classical self-dual Yang-Mills equation · Coverings and the recursion operator for full-fledged nonlocal symmetries of the rYME · 0.92