Hamiltonian systems with several space variables: dressing, explicit solutions and energy relations

Abstract

We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables $\frac{\partial \psi }{\partial t}={\sum }_{k=1}^r{H}_k(t)\frac{\partial \psi }{\partial {\zeta }_k}$ $(H_k(t)=H_k(t{)}^{\ast })$. In particular, such systems are analogs of the port-Hamiltonian systems in the important and insufficiently studied case of several space variables. The corresponding energy relations are written down. The method is illustrated by several examples, where explicit solutions are given.

The paper contains modification and important further development of some approaches presented in arXiv:2107.00435v2. This is the second version of the paper with minor improvements and corrections

References in corpus (2)

• Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
• Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications