Canonical Hamiltonians for waves in inhomogeneous media

TL;DR

This paper derives a canonical Hamiltonian form for linear waves in weakly inhomogeneous media using WKB and canonical transformations, facilitating the study of weakly nonlinear wave turbulence.

Contribution

It introduces a novel method to obtain a canonical form of the Hamiltonian for inhomogeneous wave systems, enabling advanced analysis of nonlinear wave interactions.

Findings

Canonical Hamiltonian form derived for inhomogeneous media

Method applicable to various wave systems

Foundation for weakly nonlinear wave turbulence theory

Abstract

We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the WKB representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of canonical Bogolyubov-type and near-identical transformations. Various examples of the application illustrating the main features of our approach are presented. The knowledge of the Hamiltonian structure for linear wave systems provides a basis for developing a theory of weakly nonlinear random waves in inhomogeneous media generalizing the theory of homogeneous wave turbulence.