ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The sine–Gordon and φ-four kinks are known to be reflectionless by virtue of the fact that their small oscillations are governed by the modified Pöschl–Teller potential Ul(x) =1−[(l+1)/l]sech2(x/l), with l=1 and 2, respectively. An infinite class of parent potentials Vl(φ) analogous to V1∼1−cos φ for sine–Gordon kinks and V2∼(1−φ2)2 for φ-four kinks, which bear reflectionless kinks, are constructed. This is done by requiring the lowest bound-state eigenfunction of Ul(x) to be proportional to the spatial derivative of the kink waveform φ(l)K(x), i.e., the translational mode of the kink. The resulting differential equation is solved for Vl(φ) to find that it can be expressed in terms of the student's t distribution of probability theory. Various properties of the parent potentials and their reflectionless kinks are discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527476
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