On the wave operators for the critical nonlinear Schr\"odinger equation

• Autores: Rémi Carles, Tohru Ozawa
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 1, 2008, págs. 185-195
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n1.a15
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• Resumen

  • We prove that for the $L^2$-critical nonlinear Schr\"odinger equations, the wave operators and their inverse are related explicitly in terms of the Fourier transform. We discuss some consequences of this property. In the one-dimensional case, we show a precise similarity between the $L^2$-critical nonlinear Schr\"odinger equation and a nonlinear Schr\"odinger equation of derivative type