Solitons for the Schrödinger flows on Hermitian symmetric spaces

We use loop group factorizations to construct Darboux transformations, Permutability formulas, Scaling Transformations, and explicit soliton solutions of the [Formula: see text]-d Schrödinger flows on compact Hermitian symmetric spaces.

ON GROUP FACTORIZATIONS USING FREE MAPPINGS

We say that a collection of subsets α = [B1,…, Bk] of a group G is a factorization if G = B1,…,Bk and each element of G is expressed in a unique way in this product. By using a special type of mappings between groups A and B, called free mappings, we exhibit an algorithmic way to construct nontrivial factorizations of a group G, such that G ≅ A × B. In Lemma 3.2 we give a simple way to construct free mappings. It turns out that this approach has greater importance when G is an abelian group. We give illustrative examples of this method in the cases ℤp × ℤp and ℤp × ℤq where p and q are different prime numbers. An interesting connection between free mappings and Rédei's theorem, with a number theoretic implication, is given.