On the Quadratic Bundles Related to Hermitian Symmetric Spaces

Remarks on quadratic bundles related to Hermitian symmetric spaces

“…We have discussed the spectral properties of the scattering operator L. In this sense our results generalize those obtained by Gerdjikov et al in [5,6] treating the scalar case as well as author's in [20] treating spaces of the type SU (n)/S(U (1) × U (n − 1)).…”

“…Our purpose here is to shed some light on certain basic properties of equation (5) and the corresponding Lax pair. In doing so we shall partially extend some results already published in [20]. The report is structured as follows.…”

“…they depend on t only, see [20] for more detailed explanations. F 0,k turn out to be exponential functions on time and one can propose the following simple rule…”

“…One application of the fundamental analytic solutions is in spectral theory of the scattering operator L(λ) [20]. The resolvent of L(λ) is defined by…”

Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

“…In this section we shall introduce some basic notions of direct scattering problem for quadratic bundles related to symmetric spaces of the type SU(m + n)/S(U(m) × U(n)), and sketch some of their properties. In doing this we are going to use some results and conventions from [12,16,31]. Let us consider the following Lax pair:…”