Parent potentials for an infinite class of reflectionless kinks
S. E. Trullinger, R. J. Flesch
Source abstract
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.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.