Title: Dynamical and variational properties of KdV multi-solitons
 
 Abstract:

 Since the discovery of the inverse-scattering method of solution for
 the KdV equation in the 1960's, it has been known that KdV
 multi-soliton solutions are closely related to the family of
 conserved functionals associated with the KdV hierarchy.  More
 precisely, it has been known that multi-soliton profiles are
 stationary points for the problem of varying one functional in the
 hierarchy while holding a fixed number of others constant.  Later,
 Maddocks and Sachs showed that multi-soliton profiles are local
 minimizers for such variational problems. We show that at least in
 some cases, the multi-soliton profiles are in fact global minimizers.
 The proof uses concentration compactness techniques, but is
 complicated by the fact that, in general , minimizing sequences can
 lose compactness in fairly non-trivial ways.