Deformations of the Monge/Riemann hierarchy and approximately integrable systems

Source abstract

Dispersive deformations of the Monge equation ut=uux are studied using ideas originating from topological quantum field theory and the deformation quantization program. It is shown that, to a high order, the symmetries of the Monge equation may also be appropriately deformed, and that, if they exist at all orders, they are uniquely determined by the original deformation. This leads to either a new class of integrable systems or to a rigorous notion of an approximate integrable system. Quasi-Miura transformations are also constructed for such deformed equations.