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 cubic Szeg\"o equation
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abstract
We derive an explicit formula for the general solution of the cubic Szeg\"o equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are quasiperiodic.
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2025 1verdicts
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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.