Abstract:
We consider a third-order generalized Monge–Ampère equation $u_{yyy}- u_{xxy}^2+u_{xxx}u_{xyy}=0$, which is closely related to the associativity equation in two-dimensional topological field theory. We describe all integrable structures related to it: Hamiltonian, symplectic, and also recursion operators. We construct infinite hierarchies of symmetries and conservation laws.