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

2022/10/31 by Sakhnovich, Alexander
#37J06 #37N35 #70S10 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2210.17492

Abstract

We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables (∂ ψ)/(∂ t)=∑_k=1^r H_k(t)(∂ ψ)/(∂ ζ_k) ( H_k(t)= H_k(t)^*). 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.

Related

• Generalization of the Darboux transformation and generalized harmonic oscillators
• Symmetric Hamiltonian of the Garnier system and its degenerate systems in two variables
• Multi-Hamiltonian formulation for a class of degenerate completely integrable systems
• Generation of solutions of the Hamilton-Jacobi equation
• The families of Hamiltonians sharing common symmetry structure