Indeed, since the particle radius is small, the related contribution of the correlation function to all relevant integrals should be negligible.
The system has the following integrals of motion.
In this case we find exact solutions in terms of elliptic integrals of the fir st kind.
There must be two linearly independent particular integrals, because the differential equation (46) is of order two.
Results are expressed in terms of integrals involving eigenfunctions and trapped oscillation field structures, although explicit expressions for these cannot be given.
Taking this approximation into account, we can easily calculate the integrals in (16).
The equations of motion admit the six known integrals.
The sound radiation associated with the instability wave can be found by evaluating the integrals of equation (3.20).
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