Nonlinear Fourier transform of time-limited and one-sided signals

DOI10.1088/1751-8121/aad9abzbMath1410.78025arXiv1806.03877OpenAlexW3099214608MaRDI QIDQ3120021

Vishal Vaibhav

Publication date: 28 February 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.03877

zbMATH Keywords

nonlinear opticsinverse scatteringintegrable nonlinear partial differential equation

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Second-order nonlinear hyperbolic equations (35L70) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Lasers, masers, optical bistability, nonlinear optics (78A60) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items

Nonlinearly bandlimited signals ⋮ Fast algorithms for solving the inverse scattering problem for the Zakharov-Shabat system of equations and their applications ⋮ Discrete Darboux transformation for Ablowitz-Ladik systems derived from numerical discretization of Zakharov-Shabat scattering problem

Uses Software

• DLMF

Cites Work

• Convolution quadrature and discretized operational calculus. I
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• On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations
• Exact solution of the Zakharov-Shabat scattering problem for doubly-truncated multisoliton potentials
• Darboux transformations in integrable systems. Theory and their applications to geometry
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Half-solitons as solutions to the Zakharov-Shabat eigenvalue problem for rational reflection coefficient. II. Potentials on infinite support
• Inverse scattering for an AKNS problem with rational reflection coefficients
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