The Multidimensional Darboux Transformation
High Energy Physics - Theory
2016-08-15 v1 dg-ga
Mathematical Physics
Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of dimension n greater than one. New examples of quasi-exactly solvable multidimensional matrix Schr\"odinger operators on curved manifolds are obtained by applying the above results.
Cite
@article{arxiv.hep-th/9612100,
title = {The Multidimensional Darboux Transformation},
author = {Artemio González-López and Niky Kamran},
journal= {arXiv preprint arXiv:hep-th/9612100},
year = {2016}
}
Comments
plain TeX, 29 pages. Auxiliary file Darboux.ref and macros file ao.tex