Classification of Multidimensional Darboux Transformations: First Order and Continued Type

Symmetry Integrability and Geometry-Methods and Applications

article

David Hobby¹  Ekaterina Shemyakova¹ 

[1] Department of Mathematics, State University of New York at New Paltz

关键词: Darboux transformations;    Laplace transformations;    linear partial dif ferential operators;    continued Darboux transformations;   

DOI  :  10.3842/SIGMA.2017.010

来源: National Academy of Science of Ukraine

【 摘 要 】

We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a complete description of all possible first-order Darboux transformations. We introduce a large class of invertible Darboux transformations of higher order, which we call Darboux transformations of continued Type I. This generalizes the class of Darboux transformations of Type I, which was previously introduced. There is also a modification of this type of Darboux transformations, continued Wronskian type, which generalize Wronskian type Darboux transformations.

【 授权许可】

Unknown