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arXiv · 2606.13446

Integrable metrics with potentials on the Hardy space and a class of PDEs

A. Konyaev·P. Topalov
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Abstract

We introduce a new class of quadratic in the momenta Hamiltonians with potential on Banach spaces of infinite dimension which possess an infinite family of conserved quantities in involution with respect to a naturally defined Poisson structure. We show that the Hamiltonian flows of the constructed integrals are locally well defined and that they are related to a hierarchy of evolution PDEs via nonlinear analytic transformations of the phase space, called $Q$-transforms. Our framework offers a new geometric interpretation of hierarchies of integrable PDEs, linking infinite-dimensional phase spaces directly to the classical geometric phenomenon of geodesic equivalence.

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A. Konyaev, P. Topalov. 2026-06-11. Integrable metrics with potentials on the Hardy space and a class of PDEs. https://arxiv.org/abs/2606.13446

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