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A variational formulation of three–dimensional steady water waves

We are concerned with a three–dimensional layer of a perfect and irrotational liquid of density one (e.g. water) in a gravity field pointing vertically downwards. The layer is of infinite depth and bounded above by a free surface. Babenko developed a variational theory of steady periodic two–dimensional water waves without surface tension, and the aim of this paper is to extend Babenko's formulation to three–dimensional steady periodic waves.