Davide Masoero

Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras.

The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseudo-differential operators resemble in form the Miura-transformed Lax operators studied in work on generalised KdV equations, classical W-algebras and, more recently, in the context of the geometric Langlands correspondence. Negative-dimension and boundary-condition dualities are also observed.

Poles of integrále tritronquée and anharmonic oscillators. A WKB approach

Poles of solutions to the Painleve-I equations are intimately related to the theory of the cubic anharmonic oscillator. In particular, poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We analyze this pair of quantization conditions by means of a suitable version of the complex WKB method.

Poles of intégrale tritronquée and anharmonic oscillators. Asymptotic localization from WKB analysis

Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles are well approximated by solutions of a pair of Bohr–Sommerfeld quantization conditions (the Bohr–Sommerfeld–Boutroux (B–S–B) system): the distance between a pole and the corresponding solution of the B–S–B system vanishes asymptotically.

Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case

We assess the ODE/IM correspondence for the quantum

Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe

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Critical behavior for scalar nonlinear waves

g-KdV model, for a non-simply laced Lie algebra

ABCD and ODEs

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