The Multidimensional Darboux Transformation
González-López, Artemio ; Kamran, Niky
arXiv, 9612100 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1996-12-10
Classification:  High Energy Physics - Theory,  Mathematical Physics,  Mathematics - Differential Geometry,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{9612100,
     author = {Gonz\'alez-L\'opez, Artemio and Kamran, Niky},
     title = {The Multidimensional Darboux Transformation},
     journal = {arXiv},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9612100}
}

González-López, Artemio; Kamran, Niky. The Multidimensional Darboux Transformation. arXiv, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/9612100/