# On the analyticity of the Dirichlet–Neumann operator and Stokes waves

@article{Berti2022OnTA, title={On the analyticity of the Dirichlet–Neumann operator and Stokes waves}, author={Massimiliano Berti and A. Maspero and Paolo Ventura}, journal={Rendiconti Lincei - Matematica e Applicazioni}, year={2022} }

We prove an analyticity result for the Dirichlet-Neumann operator under space periodic boundary conditions in any dimension in an unbounded domain with infinite depth. We derive an analytic bifurcation result of analytic Stokes waves –i.e. space periodic traveling solutions– of the water waves equations in deep water. MSC 2020: 76B15, 35B32, 35J05.

## One Citation

### Benjamin-Feir instability of Stokes waves in finite depth

- Mathematics
- 2022

Whitham and Benjamin predicted in 1967 that small-amplitude periodic traveling Stokes waves of the 2d-gravity water waves equations are linearly unstable with respect to long-wave perturbations, if…

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