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Let us split into its real and imaginary parts
and
. Then the equation () splits into two
coupled equations
where we have used the fact that
, which follows from
().
Gabor transforming our two coupled equations () and
() and using Taylor series to represent large-scale
quantities,
we find
Where
is the Gabor transform of . We have kept
only
terms and neglected the
and
higher order terms. For generality, we have kept the nonlinear term.
Subsections
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Dr Yuri V Lvov
2007-01-23