ISSN:
1573-9333
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
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)=p 3Ω(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 functionp 3Ω(q/p) of polynomial form is found.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01015890
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