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2007•EPrints - Department of Mathematics, Hokkaido UniversityOpen access

On the wave operators for the critical nonlinear Schrodinger equation

Rémi Carles, Tohru Ozawa

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Abstract

We prove that for the mass critical nonlinear Schrodinger 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 mass critical nonlinear Schrodinger equation and a nonlinear Schrodinger equation of derivative type.

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We prove that for the mass critical nonlinear Schrodinger 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 mass critical nonlinear Schrodinger equation and a nonlinear Schrodinger equation of derivative type.

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Available abstract

We prove that for the mass critical nonlinear Schrodinger 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 mass critical nonlinear Schrodinger equation and a nonlinear Schrodinger equation of derivative type.

Key concepts: Nonlinear Schrödinger equation, Schrödinger equation, Nonlinear system, Split-step method, Mathematics, Schrödinger's cat, Fourier transform, Mathematical analysis

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