Change search
ReferencesLink to record
Permanent link

Direct link
Solitons and the removal of eigenvalues for fourth-order differential operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2006 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247Article in journal (Refereed) Published
Abstract [en]

A nonlinear functional Q[u, v] is given that governs the loss, respectively gain, of ( doubly degenerate) eigenvalues of fourth-order differential operators L = partial derivative(4) + partial derivative u partial derivative + 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 the eigenfunctions of L, we find u and v such that L is isospectral to the free operator L-0 = partial derivative(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. Removal of eigenvalues allows us to obtain a sharp Lieb-Thirring inequality for a class of operators L whose negative eigenvalues are of multiplicity two.

Place, publisher, year, edition, pages
URN: urn:nbn:se:kth:diva-15956ISI: 000240181600001ScopusID: 2-s2.0-33747029312OAI: diva2:333998
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

Open Access in DiVA

No full text


Search in DiVA

By author/editor
Hoppe, JensLaptev, Ari
By organisation
Mathematics (Div.)
In the same journal
International mathematics research notices

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 18 hits
ReferencesLink to record
Permanent link

Direct link