Degenerate multidimensional dispersion laws
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Abstract
A study is made of the degeneracy of multidimensional dispersion laws ω(k) that increase unboundedly as ⥻k⥻→∞ and satisfy some additional conditions. Under the assumption that the corresponding degeneracy functionf(k) satisfies a certain condition [Eq. (4)], it is shown that only two-dimensional dispersion laws of the form ω(p,q)=p3Ω(q/p)+cp↓(q/p)(|p|,|q|≪1), wherepψ(q/p)=f(p, q) is the corresponding unique degeneracy function, can be degenerate with respect to a 1→2 process. Some conditions that the function Ω(ξ) must satisfy are obtained. The explicit form of a degenerate dispersion law with functionp3Ω(q/p) of polynomial form is found.
Keywords
Explicit Form Additional Condition Polynomial Form Degeneracy Function Unique Degeneracy
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© Plenum Publishing Corporation 1993