Almost integrable evolution equations

Integrable geometric evolution equations for curves

The vortex filament flow and planar filament flow are examples of evolution equations which commute with Euclidean isometries and are also integrable, in that they induce completely integrable PDE for curvature—the focusing nonlinear Schödinger equation and the mKdV equations, respectively. In this note we outline an approach for classifying integrable geometric evolution equations for planar c...

Integrable Evolution Equations in Time-Dependent Domains

Local Geometric Invariants of Integrable Evolution Equations

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.

Classification of Symmetry-Integrable Evolution Equations

This paper describes some recent developments which have made it possible to effectively classify homogeneous systems having infinitely many generalized symmetries, both in the commutative and the noncommutative case. It discusses the program that has to be carried out next to come to an automatic classification mechanism.

Almost Periodicity of Inhomogeneous Parabolic Evolution Equations