-deformation of the Virasoro algebra and lattice conformal theories
-deformed KP hierarchy and -deformed constrained KP hierarchy.
Quantum curve in -oscillator model.
Quantum integrable systems
Quantum relativistic Toda chain.
Quasiclassical limit of KP hierarchy, -symmetries, and free fermions
Quasigraded Lie algebras and modified Toda field equations.
Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
A lattice model with exponential interaction, was proposed and integrated by M. Toda in the 1960s; it was then extensively studied as one of the completely integrable (differential-difference) equations by algebro-geometric methods, which produced both quasi-periodic solutions in terms of theta functions of hyperelliptic curves and periodic solutions defined on suitable Jacobians by the Lax-pair method. In this work, we revisit Toda’s original approach to give solutions of the Toda lattice in terms...
Quasi-periodic solutions of Hamiltonian PDEs
We overview recent existence results and techniques about KAM theory for PDEs.
Quasi-periodic solutions with Sobolev regularity of NLS on with a multiplicative potential
We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are then the solutions are . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...