**Boris Gershgorin
, Yuri V. Lvov
, and Sergey Nazarenko
,**

*Courant Institute, New York University, New York, NY
10012, USA*

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.

- Introduction
- Motivation

- Preliminaries
- The case of nearly-diagonal Hamiltonians.
- Formulation and Proof of the Lemma
- Relation to the Wigner Transformation
- Example: Linear Schrödinger equation
- Example: an advection-type system

- General case of waves in weakly-inhomogeneous media

- Conclusions

- Window transform
- Calculation of
- Bogolyubov transformation of the part
- Canonicity conditions for near-identity transformation
- Near-identity transformation
- Bibliography
- About this document ...

Dr Yuri V Lvov 2008-07-08