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It is interesting to notice that a quick but fallacious back of the envelope argument applied to Eq. (4.1) in the limit [Formula Presented] where [Formula Presented] vanishes, yields the complex dispersion law [Formula Presented] The correct result [Formula Presented] following from Eq. (4.3) is, of course, due to the influence of the term [Formula Presented] at long distances
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It is interesting to notice that a quick but fallacious back of the envelope argument applied to Eq. (4.1) in the limit x→±∞, where ∇u0 vanishes, yields the complex dispersion law ω=-iνk2-λu0k. The correct result ω=-iν(k2+ks2), following from Eq. (4.3) is, of course, due to the influence of the term ∇u0∝cosh-2[ks(x-x0)] at long distances.
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