Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisited
arXiv:0804.2020 · doi:10.1007/s10440-009-9452-2
Abstract
We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4α)z z_x, z_t &=& (1-2α)z_{xx} - 4αz w_x + (4-8α)w z_x - (4+8α)w^2 z + (-2+4α)z^3, (*) for which no recursion operator or master symmetry was known so far, and prove that the system (*) admits infinitely many local generalized symmetries that are constructed using a nonlocal {\em two-term} recursion relation rather than from a recursion operator.
10 pages, LaTeX; minor changes in terminology; some references and definitions added