Abstract
The classical irrotational water wave problem described by Euler equations with a nonlinear free surface boundary condition and influenced by gravity over a flat bed is considered. Exploiting the monotonicity property of the flow force lines with depth, the unknown boundary problem is transformed into a problem with fixed domain. A flow force function formulation of the irrotational water wave problem is developed. Variational approach is used to prove the existence of small amplitude irrotational traveling wave solutions. Local bifurcation results have been proved relying on Crandall-Rabinowitz bifurcation theorem.
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