When
we have Hamiltonian in a form

Equation of motion is mostly conveniently represented in the interaction representation,

where is the complex wave amplitude in the interaction representation, are the indices numbering the wavevectors, e.g. , is the box side length, and is the wave linear dispersion relation. Here, is an interaction coefficient and is introduced as a formal small nonlinearity parameter.

Dr Yuri V Lvov 2007-01-23