Equation (4.2) is satisfied by the expression
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(5.4) |
Using (4.7) and (5.3) the left hand side of (4.3) is expressed as
With (4.6), (4.8), and (5.5) the right hand side of (4.3) is given by
Substituting (5.6) and (5.7) in (4.3)
the following equation for
and
in the frequency domain is obtained
Analogously after partial differentiation of (4.4) with respect to time and using (4.5), (4.6), and (4.8) it can be written
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(5.9) |
Equation (5.10) can also be obtained by applying the
divergence operator to (5.8). The unknown fields
and
are obtained from the boundary value
problem given by the partial differential equation
system (5.8) and (5.10). A similar
strategy can be found in [67,68],
where
and the
auxiliary arbitrary scalar field
is conveniently termed as a ghost field.