We review the notion of differential Fay identities and demonstrate, through case studies, its new role in integrable hierarchies of the KP type. These identities are known to be a convenient tool for deriving dispersionless Hirota equations. We show that differential (or, in the case of the Toda hierarchy, difference) Fay identities play a more fundamental role. Namely, they are nothing but a ...

Connections of KP, qKP, and Moyal type dKP constructions are developed. Some expansion of the Moyal KP constructions of Kemmoku-Saito is given with clarification of the role of spectral variables as a phase space.

We review the notion of differential Fay identities and demonstrate, through case studies, its new role in integrable hierarchies of the KP type. These identities are known to be a convenient tool for deriving dispersionless Hirota equations. We show that differential (or, in the case of the Toda hierarchy, difference) Fay identities play a more fundamental role. Namely, they are nothing but a ...

The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for the construction classes of nontrivial solutions of the dKP equation.

Michael addition reactions of triketopiperazine (TKP) derivatives to enones, mediated by a cinchona alkaloid-derived catalyst, deliver products in high yield and enantiomeric ratio (er). Use of unsaturated ester, nitrile or sulfone partners gives bridged hydroxy-diketopiperazine (DKP) products resulting from a novel Michael addition-ring closure.

We prove the equivalence of many-gluon Green functions in DuffinKemmer-Petieu (DKP) and Klein-Gordon-Fock (KGF) statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their e...

A class of Einstein–Weyl spaces associated to an integrable system of hydrodynamic type. Abstract HyperCR Einstein–Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can be in principle constructed from a twistor correspondence, thus establishing the integrability. Simple examples of solutions including the hydr...