Semiclassical spectral confinement for the sine-Gordon equation

Robert Buckingham

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 6, 1030-1037

Abstract: The inverse scattering method for solving the sine-Gordon equation in laboratory coordinates requires the analysis of the Faddeev–Takhtajan eigenvalue problem. This problem is not self-adjoint and the eigenvalues may lie anywhere in the complex plane, so it is of interest to determine conditions on the initial data that restrict where the eigenvalues can be. We establish bounds on the eigenvalues for a broad class of zero-charge initial data that are applicable in the semiclassical or zero-dispersion limit. It is shown that no point off the coordinate axes or turning point curve can be an eigenvalue if the dispersion parameter is sufficiently small.

Keywords: Sine-Gordon; Semiclassical problems; Eigenvalues; Inverse scattering (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475410002259
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:6:p:1030-1037

DOI: 10.1016/j.matcom.2010.07.002

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().