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March/April 2014 A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D
Soichiro Katayama, Chunhua Li, Hideaki Sunagawa
Differential Integral Equations 27(3/4): 301-312 (March/April 2014).

Abstract

We consider the initial value problem for a three-component system of quadratic nonlinear Schrödinger equations with mass resonance in two space dimensions. Under a suitable condition on the coefficients of the nonlinearity, we will show that the solution decays strictly faster than ${O(t^{-1})}$ as $t \to +\infty$ in $L^{\infty}$ by providing an enhanced decay estimate of order $O((t\log t)^{-1})$. Differently from the previous works, our approach does not rely on the explicit form of the asymptotic profile of the solution at all.

Citation

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Soichiro Katayama. Chunhua Li. Hideaki Sunagawa. "A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D." Differential Integral Equations 27 (3/4) 301 - 312, March/April 2014.

Information

Published: March/April 2014
First available in Project Euclid: 30 January 2014

zbMATH: 1324.35170
MathSciNet: MR3161606

Subjects:
Primary: 35B40, 35Q55

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 3/4 • March/April 2014
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