Differential and Integral Equations

On a system of nonlinear Schrödinger equations in 2d

Nakao Hayashi, Chunhua Li, and Pavel I. Naumkin

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Abstract

We consider a system of nonlinear Schrödinger equations with quadratic nonlinearities in two space dimensions. Our aim is to show time decay estimates of small solutions and nonexistence of the usual scattering states for a system. Furthermore we prove stability in time of small solutions in the neighborhood of solutions to a suitable approximate equation.

Article information

Source
Differential Integral Equations, Volume 24, Number 5/6 (2011), 417-434.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356018911

Mathematical Reviews number (MathSciNet)
MR2809614

Zentralblatt MATH identifier
1249.35305

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35B40: Asymptotic behavior of solutions

Citation

Hayashi, Nakao; Li, Chunhua; Naumkin, Pavel I. On a system of nonlinear Schrödinger equations in 2d. Differential Integral Equations 24 (2011), no. 5/6, 417--434. https://projecteuclid.org/euclid.die/1356018911


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