Integrable zero-range potentials in a plane

Physics and Mathematics of Nonlinear Phenomena 2013

Leble, S.^1

Gdansk University of Technology, ul. Narutowicza 11/12, Gdansk, 80-952, Poland^1

关键词: A-plane;    Darboux transform;    Darboux transformations;    Long waves;    Scattering problems;    Underlying distribution;    Zero-range potentials;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012025/pdf
DOI  :  10.1088/1742-6596/482/1/012025

来源: IOP

【 摘 要 】

We examine general statements in the Wronskian representation of Darboux transformations for plane zero-range potentials. Such expressions naturally contain scattering problem solution. We also apply Abel theorem to Wronskians for differential equations and link it to chain equations for Darboux transforms to fix conditions for further development of the underlying distribution concept. Moutard transformations give a convenient insight into the problem that allows one to formulate general assertions and give complete description of a point potential in a limit of long waves.