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In particular, for the wave kinetic equations of energies, only the interactions between nonlinear terms involving either energies or helicities will give a contribution.
Since the wave interaction equations are linear the scattering matrix (5.23) gives the solution for c (t) for general initial data c (0).
We have also obtained a solution of these model e equations.
The characteristic equations (4.48)-(4.50) do not take into account the symmetry of the fluid frame group velocity surface about the magnetic field.
All of these terms are expressed as functions of through the energ y equations (3.1a)-(3.1d).
The system of the evolution equations, (2.6)-(2.8), will be the basis of the analysis that follows.
The coefficients of the wave equations depend on time through the wave vector, which includes the stretch effect by the rotation shear.
We conclude this introduction with a statement of the gover ning equations.
From this model two coupled differential equations for the parallel ion velocity and the perturbed electrostatic potential were derived.
We present the corresponding equations at the end of the appendix.
In this section, however, we give the equations describing the stability of a general rotating plasma column.
Using these equations, we can find the flow in the physical plane.
To describe small-amplitude wave-like phenomena, the basic equations are linearized.
An iterative scheme is used to solve the linearized system of difference equations.
The work is suitable for a general audience, as equations have been consigned to a comprehensive mathematical appendix.
