Recursion without recursion operator: the Foursov–Burgers system revisited

We show that the Burgers-type system studied by Foursov
w_t & = w_xx + 8 w w_x + (2-4 α)z z_x,
z_t & = (1-2 α)z_xx - 4 α z w_x + (4-8 α)w z_x - (4+8 α)w² z + (-2+4 α)z³, (*)
for which no recursion operator was known so far, is C-integrable and can be reduced to a triangular form via a suitable differential substitution. Moreover, we show that (*) admits infinitely many local generalized symmetries that are constructed using a nonlocal two-term recursion relation rather than a recursion operator.