Print Email Facebook Twitter Fast inverse nonlinear Fourier transform Title Fast inverse nonlinear Fourier transform Author Vaibhav, V.K. (TU Delft Team Raf Van de Plas) Date 2018 Abstract This paper considers the non-Hermitian Zakharov-Shabat scattering problem which forms the basis for defining the SU(2)-nonlinear Fourier transform (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transform is quite well established in the Ablowitz-Kaup-Newell-Segur formalism; however, efficient numerical algorithms that could be employed in practical applications are still unavailable. In this paper, we present two fast inverse NFT algorithms with O(KN+Nlog2N) complexity and a convergence rate of O(N-2), where N is the number of samples of the signal and K is the number of eigenvalues. These algorithms are realized using a new fast layer-peeling (LP) scheme [O(Nlog2N)] together with a new fast Darboux transformation (FDT) algorithm [O(KN+Nlog2N)] previously developed by V. Vaibhav [Phys. Rev. E 96, 063302 (2017)2470-004510.1103/PhysRevE.96.063302]. The proposed fast inverse NFT algorithm proceeds in two steps: The first step involves computing the radiative part of the potential using the fast LP scheme for which the input is synthesized under the assumption that the radiative potential is nonlinearly bandlimited, i.e., the continuous spectrum has a compact support. The second step involves addition of bound states using the FDT algorithm. Finally, the performance of these algorithms is demonstrated through exhaustive numerical tests. To reference this document use: http://resolver.tudelft.nl/uuid:d70a0753-ba3d-4ddd-a638-bbd7357fcb93 DOI https://doi.org/10.1103/PhysRevE.98.013304 ISSN 2470-0045 Source Physical Review E, 98 (1) Part of collection Institutional Repository Document type journal article Rights © 2018 V.K. Vaibhav Files PDF PhysRevE.98.013304.pdf 1.38 MB Close viewer /islandora/object/uuid:d70a0753-ba3d-4ddd-a638-bbd7357fcb93/datastream/OBJ/view