The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
An explicit formula for the Benjamin–Ono equation
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Proves wellposedness in H^{-1} for the full KdV hierarchy by relating it to the Gardner hierarchy via the Miura map and applying Kato smoothing estimates.
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A superintegrable quantum field theory
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
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Wellposedness for the KdV hierarchy
Proves wellposedness in H^{-1} for the full KdV hierarchy by relating it to the Gardner hierarchy via the Miura map and applying Kato smoothing estimates.