English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Darboux transformations are non-group type symmetries of linear differentialoperators. One can define Darboux transformations algebraically by theintertwining relation $ML=L_1M$ or the intertwining relation $ML=L_1N$ in thecases when the first one is too restrictive.  Here we show that Darboux transformations for operators of the form$\partial_x\partial_y +a \partial_x + b\partial_y +c$ (often referred to as 2DSchr\"odinger operators) are always compositions of atomic Darbouxtransformations of two different types. This is in contrast with the case of 1DSchr\"odinger operators and other 1D operators, where there is only one atomickind of Darboux transformations.

Classification of Darboux transformations for operators of the form $\partial_x\partial_y +a \partial_x + b\partial_y +c$