Complex nonlinear Fourier transform and its inverse

30th International Colloquium on Group Theoretical Methods in Physics

Saksida, Pavle^1,2

Faculty of Mathematics and Physics, University of Ljubljana, Slovenia^1

Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia^2

关键词: Convergent series;    Explicit algorithms;    Integrable systems;    Nonlinear fourier transforms;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012066/pdf
DOI  :  10.1088/1742-6596/597/1/012066

来源: IOP

【 摘 要 】

We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform Fc. We construct an explicit algorithm for the calculation of the inverse transform (Fc)-1(h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations.