Follytons and the Removal of Eigenvalues for Fourth Order Differential Operators

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dc.creatorHoppe, Jens
dc.creatorLaptev, Ari
dc.creatorOstensson, Jorgen
dc.date2003-11-09
dc.date.accessioned2026-07-07T04:30:42Z
dc.date.available2026-07-07T04:30:42Z
dc.descriptionA non-linear functional $Q[u,v]$ is given that governs the loss, respectively gain, of (doubly degenerate) eigenvalues of fourth order differential operators $L = \partial^4 + \partial u \partial + v$ on the line. Apart from factorizing $L$ as $A^{*}A + E_{0}$, providing several explicit examples, and deriving various relations between $u$, $v$ and eigenfunctions of $L$, we find $u$ and $v$ such that $L$ is isospectral to the free operator $L_{0} = \partial^{4}$ up to one (multiplicity 2) eigenvalue $E_{0} < 0$. Not unexpectedly, this choice of $u$, $v$ leads to exact solutions of the corresponding time-dependent PDE's.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0311011
dc.identifierhttp://arxiv.org/abs/math-ph/0311011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57556
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject34L40 (Primary), 34L30 (Secondary)
dc.titleFollytons and the Removal of Eigenvalues for Fourth Order Differential Operators
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