The stability of periodic solutions of partial differential equations has been an area of increasing interest in the last decade. In this paper, we derive all periodic traveling wave solutions of the focusing and defocusing mKdV equations. We show that in the defocusing case all such solutions are orbitally stable with respect to subharmonic perturbations: perturbations that are periodic with p...

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...

Based on the factorization of soliton equations into two commuting integrable xand t-constrained flows, we derive N -soliton solutions for mKdV equation via its xand t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.

We present a review of the Symmetric Unitary One Matrix Models. In particular we compute the scaling operators in the double scaling limit and the corresponding mKdV ows. We brieey discuss the computation of the space of solutions to the string equation as a subspace of Gr (0)

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...