On Plancherel's identity for a two-dimensional scattering transform

Kari Astala, Daniel Faraco, Keith M. Rogers

Type: Article

Publication Date: 2015-06-30

Citations: 6

DOI: https://doi.org/10.1088/0951-7715/28/8/2721

Abstract

We consider the -Dirac system that Ablowitz and Fokas used to transform the defocussing Davey–Stewartson system to a linear evolution equation. The nonlinear Plancherel identity for the associated scattering transform was established by Beals and Coifman for Schwartz functions. Sung extended the validity of the identity to functions belonging to and Brown to L2-functions with sufficiently small norm. More recently, Perry extended to the weighted Sobolev space and here we extend to with 0 < s < 1.

Locations

Nonlinearity - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (16)

Action	Title	Year	Authors
+	Nonlinear evolution equations : integrability and spectral methods	1990	A. Degasperis Allan P. Fordy Muthuswamy Lakshmanan
+	Classical Fourier Analysis	2014	Loukas Grafakos
+	Global Well-Posedness and Long-time Asymptotics for the Defocussing Davey-Stewartson II Equation in $H^{1,1}(R^2)$	2011	Peter Perry
+ PDF Chat	The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals	2007	Jonathan Bennett Anthony Carbery Michael Christ Terence Tao
+ PDF Chat	Bilinear Sobolev–Poincaré Inequalities and Leibniz-Type Rules	2012	Frédéric Bernicot Diego Maldonado Kabe Moen Virginia Naibo
+	An Inverse Scattering Transform for the Davey-Stewartson II Equations, III	1994	Li-yeng Sung
+ PDF Chat	Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities	2010	Jonathan Bennett Anthony Carbery Michael Christ Terence Tao
+	WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for One-Dimensional Schrödinger Operators with Slowly Decaying Potentials	2001	Michael Christ Alexander Kiselev
+ PDF Chat	Estimates for the Scattering Map Associated with a Two-Dimensional First-Order System	2001	R. M. Brown
+	On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane	1984	A. S. Fokas Mark J. Ablowitz