On the Spectral Properties of Lax Operators Related to BD.I Symmetric Spaces

摘要

We consider a class of Lax operators L related to BD.I type symmetric spaces. They allow one to solve a special class of vector NLS equations which model Bose-Einstein condensates with spin. We construct the kernel of the resolvent for L and prove that the fundamental analytic solutions of L satisfy completeness relation on a subspace of the vector space M.