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We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov-Witten invariants via tau-function of the(More)
An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established, this transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon(More)
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the CP 1 topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter(More)
We study the general structure of formal perturbative solutions to the Hamil-tonian perturbations of spatially one-dimensional systems of hyperbolic PDEs v t + [φ(v)] x = 0. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the(More)
We study the general structure of formal perturbative solutions to the Hamil-tonian perturbations of spatially one-dimensional systems of hyperbolic PDEs v t + [φ(v)] x = 0. Under certain genericity assumptions it is proved that any bi-Hamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the(More)