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SIGMA, 2010, Volume 6, 046, 17 pages (Mi sigma503)  

This article is cited in 3 scientific papers (total in 3 papers)

The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation

B. J. Durhuusa, V. Gayralb

a Department of Mathematics, Copenhagen University, Universitetsparken 5, DK-2100 Copenhagen ø, Denmark
b Laboratoire de Mathématiques, Université de Reims Champagne--Ardenne, Moulin de la Housse - BP 1039 51687 Reims cedex 2, France

Abstract: We investigate scattering properties of a Moyal deformed version of the nonlinear Schrödinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general initial data has a unique globally defined solution, and also has solitary wave solutions if the interaction potential is suitably chosen. We demonstrate how to set up a scattering framework for equations of this type, including appropriate decay estimates of the free time evolution and the construction of wave operators defined for small scattering data in the general case and for arbitrary scattering data in the rotationally symmetric case.

Keywords: noncommutative geometry; nonlinear wave equations; scattering theory; Jacobi polynomials

DOI: https://doi.org/10.3842/SIGMA.2010.046

Full text: PDF file (289 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/046/
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Bibliographic databases:

ArXiv: 0903.1493
MSC: 35K99; 58B34; 53D55
Received: March 3, 2010; in final form May 20, 2010; Published online June 3, 2010
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Citation: B. J. Durhuus, V. Gayral, “The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation”, SIGMA, 6 (2010), 046, 17 pp.

Citation in format AMSBIB
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\by B.~J.~Durhuus, V.~Gayral
\paper The Scattering Problem for a~Noncommutative Nonlinear Schr\"odinger Equation
\jour SIGMA
\yr 2010
\vol 6
\papernumber 046
\totalpages 17
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\crossref{https://doi.org/10.3842/SIGMA.2010.046}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Krueger A.J., Soffer A., “Structure of Noncommutative Solitons: Existence and Spectral Theory”, Lett. Math. Phys., 105:10 (2015), 1377–1398  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Lechner G., Verch R., “Linear Hyperbolic PDEs With Noncommutative Time”, J. Noncommutative Geom., 9:3 (2015), 999–1040  crossref  mathscinet  zmath  isi  elib  scopus
    3. Krueger A.J., Soffer A., “Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates”, Ann. Henri Poincare, 17:5 (2016), 1181–1208  crossref  mathscinet  zmath  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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