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- W2138851140 abstract "The study of nonlinear Schrödinger systems with quadratic interactions has attracted much attention in the recent years. In this paper, we summarize time decay estimates of small solutions to the systems under the mass resonance condition in 2-dimensional space. We show the existence of wave operators and modified wave operators of the systems under some mass conditions in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>-dimensional space, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>. The existence of scattering operators and finite time blow-up of the solutions for the systems in higher space dimensions is also shown." @default.
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- W2138851140 date "2014-01-01" @default.
- W2138851140 modified "2023-09-23" @default.
- W2138851140 title "Recent Progress on Nonlinear Schrödinger Systems with Quadratic Interactions" @default.
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- W2138851140 doi "https://doi.org/10.1155/2014/214821" @default.
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