The NLS approximation for two dimensional deep gravity waves

Mihaela Ifrim; Daniel Tataru

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arXiv · 1809.05060

The NLS approximation for two dimensional deep gravity waves

Mihaela Ifrim·Daniel Tataru

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Abstract

This article is concerned with infinite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem with small wave packet data, and to show that this is well approximated by the cubic nonlinear Schr\"odinger equation (NLS) on the natural cubic time scale.

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Mihaela Ifrim, Daniel Tataru. 2018-09-13. The NLS approximation for two dimensional deep gravity waves. https://arxiv.org/abs/1809.05060

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