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arXiv · 1408.6464

A note on decay rates of solutions to a system of cubic nonlinear Schr\"odinger equations in one space dimension

Donghyun Kim
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Abstract

We consider the initial value problem for a system of cubic nonlinear Schr\"odinger equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution exists globally and decays of the rate $O(t^{-1/2}(\log t)^{-1/2})$ in $L^\infty$ as $t$ tends to infinity, if the system satisfies certain mass relations.

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Donghyun Kim. 2014-08-27. A note on decay rates of solutions to a system of cubic nonlinear Schr\"odinger equations in one space dimension. https://doi.org/10.3233/asy-161362

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