We define hierarchies of differential–q-difference equations, which are q–deformations of the equations of the generalized KdV hierarchies. We show that these hierarchies are bihamiltonian, one of the hamiltonian structures being that of the q–deformed classical W–algebra of slN , defined by Reshetikhin and the author. We also find q–deformations of the mKdV hierarchies and the affine Toda equa...

AbstractIntegrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2– 3– dimensional Minkowski space. The derivation uses a Lorentzian version geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation nonlinear Schrodinger (NLS) Euclidean space, respectively. In 2–dimensional timelike/spacelike curve shown defocusi...

Two consistency conditions for partition functions established by Akemann and Dam-gaard in their studies of the fermionic mass dependence of the QCD partition function at low energy (a la Leutwiller-Smilga-Verbaarschot) are interpreted in terms of integrable hierarchies. Their algebraic relation is shown to be a consequence of Wick's theorem for 2d fermionic correlators (Hirota identities) in t...