Complex nonlinear Fourier transform and its inverse

Pavle Saksida

Type: Article

Publication Date: 2015-04-13

Citations: 0

DOI: https://doi.org/10.1088/1742-6596/597/1/012066

Abstract

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.

Locations

Journal of Physics Conference Series - View - PDF

Similar Works

Action	Title	Year	Authors
+	Discrete nonlinear Fourier transforms and their inverses	2022	Pavle Saksida
+	Nonlinear Fourier Analysis	2012	Terence Tao Christoph Thiele
+	Appendix B: Fourier and Chebyshev Series	2015
+	Introduction to Linear and Nonlinear Integrable Theories in Discrete Complex Analysis	2017	Ulrike Bücking
+	THE COMPLETELY INTEGRABLE SYSTEMS OF THE COMPLEX FORM AND THE COUPLED AKNS-KAUP-NEWELL EQUATION HIERARCHY	1997	张保才
+	Real Fourier series and complex Fourier series	2010	Marcus Pivato
+	Nilpotent Fourier transform and applications	1985	Didier Arnal J. C. Cortet
+	Nonlinear Fourier transforms and integrability in multidimensions	2008	A. S. Fokas
+	Reduced AKNS Spectral Problems and Associated Complex Matrix Integrable Models	2023	Wen‐Xiu Ma
+	New non-isospectral integrable couplings of the AKNS system	2008	Ye-Peng Sun Hongqing Zhao
+	Fourier Transformation of Arbitrary Analytic Functions. Complex Fourier Method	1991	Julii A. Dubinskii
+	Integrable symplectic maps associated with the ZS-AKNS spectral problem	2012	Cewen Cao Guangyao Zhang
+	Fourier and Laplace transformations	2012	Horst Osswald
+	Fourier Transformation	2003	Philippe Blanchard Erwin Brüning
+	Closed expression of the hyper-complex Fourier kernel	2017	Pan Lian
+	Complex Fourier Series	2018	Fuad Badrieh
+	Fourier series	2012	K. F. Riley M. P. Hobson
+	Integrable systems: From the inverse spectral transform to zero curvature condition	2020	Basir Ahamed Khan Supriya Chatterjee Golam Ali Sekh B. Talukdar
+ PDF Chat	The Discrete Self-Adjoint Dirac Systems of General Type: Explicit Solutions of Direct and Inverse Problems, Asymptotics of Verblunsky-Type Coefficients and the Stability of Solving of the Inverse Problem	2018	Inna Roitberg Alexander Sakhnovich
+ PDF Chat	A nonlinear identity for the scattering phase of integrable models	1998	N. A. Slavnov

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (10)

Action	Title	Year	Authors
+	Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results	1998	Michael Christ Alexander Kiselev
+	None	2002	A. S. Fokas
+	Inverse Scattering for Schrödinger Operators with Miura Potentials, II. Different Riccati Representatives	2011	Rostyslav Hryniv Yaroslav V. Mykytyuk Peter Perry
+ PDF Chat	A counterexample to a multilinear endpoint question of Christ and Kiselev	2003	Camil Muscalu Terence Tao Christoph Thiele
+	On zero-curvature condition and Fourier analysis	2011	Pavle Saksida
+	Nonlinear-Evolution Equations of Physical Significance	1973	Mark J. Ablowitz D. J. Kaup Alan C. Newell Harvey Segur
+	Maximal Functions Associated to Filtrations	2001	Michael Christ Alexander Kiselev
+ PDF Chat	Inverse scattering for Schrödinger operators with Miura potentials: I. Unique Riccati representatives and ZS-AKNS systems	2009	Christopher Frayer Rostyslav Hryniv Ya. V. Mykytyuk Peter Perry
+ PDF Chat	A Carleson type theorem for a Cantor group model of the scattering transform	2002	Camil Muscalu Terence Tao Christoph Thiele
+	Nonlinear Fourier Analysis	2012	Terence Tao Christoph Thiele