Deformations of the Monge/Riemann hierarchy and approximately integrable systems

Details Deformations of the Monge/Riemann hierarchy and approximately integrable systems Deformations of the Monge/Riemann hierarchy and approximately integrable systems

2002-05-22

arxiv.org/abs/nlin/0205051v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages LaTeX

Scientific paper

Dispersive deformations of the Monge equation u_u=uu_x are studied using ideas originating from topological quantum field theory and the deformation quantization programme. 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.

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