On the quadratic bundles related to Hermitian symmetric spaces. (English) Zbl 1312.37046

Valchev, Tihomir I.

J. Geom. Symmetry Phys. 29, 83-110 (2013).

Summary: Here we develop the direct scattering problem for quadratic bundles associated to Hermitian symmetric spaces. We adapt the dressing method for quadratic bundles which allows us to find special solutions to multicomponent derivative Schrödinger equation for instance. The latter is an infinite-dimensional Hamiltonian system possessing infinite number of integrals of motion. We demonstrate how one can derive them by block diagonalization of the corresponding Lax pair.

MSC:

37K15	Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K05	Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)

Keywords:

direct scattering problem; quadratic bundle; Hermitian symmetric space; dressing method; Hamiltonian system