Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications

Abstract

We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in this way. Interesting results for dynamical systems depending on several variables and their explicit solutions follow. For these purposes we use our version of Bäcklund-Darboux transformation and square roots of the corresponding generalised matrix eigenvalues. Some new auxiliary results on the roots of matrices are included as well. An appendix is added to make the paper self-sufficient.

This is an updated development of the previous version with applications to dynamical systems

References in corpus (4)

• Dressing Method for the Degasperis-Procesi Equation
• Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
• Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter
• Characteristic function of M. Livšic and some developments

Cited by in corpus (2)

• Explicit solutions of Schrödinger and KdV equations in terms of square roots of the generalised matrix eigenvalues
• Hamiltonian systems with several space variables: dressing, explicit solutions and energy relations