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- W2921557026 abstract "We consider the quadratic nonlinear Schr{o}dinger system (NLS system) begin{align*}begin{cases} ipartial_t u + Delta u = v overline{u}, ipartial_t v+kappa Delta v = u^2, end{cases} text{ on } I times mathbb{R}^5, end{align*} where $kappa>0$. The scattering below the standing wave solutions for NLS system was obtained by the first author when $kappa = 1/2$. The condition of $kappa=1/2$ is called mass-resonance. In this paper, we prove scattering below the standing wave solutions when $kappa neq 1/2$ under the radially symmetric assumption. Our proof is based on the concentration compactness and the rigidity by Kenig--Merle. Moreover, we discuss the concentration compactness and the rigidity for non-radial solutions." @default.
- W2921557026 created "2019-03-22" @default.
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- W2921557026 date "2019-03-14" @default.
- W2921557026 modified "2023-09-27" @default.
- W2921557026 title "Scattering for the quadratic nonlinear Schr{o}dinger system in $mathbb{R}^5$ without mass-resonance condition" @default.
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