A proof of the Benjamin-Feir instability
The existence and linear stability problem for the Stokes periodic wavetrain on fluids of finite depth is formulated in terms of the spatial and temporal Hamiltonian structure of the water-wave problem. A proof, within the Hamiltonian framework, of instability of the Stokes periodic wavetrain is presented. A Hamiltonian center-manifold analysis reduces the linear stability problem to an ordinary differential eigenvalue problem on \(\mathbb{R}^4\). A projection of the reduced stability problem onto the tangent space of the 2-manifold of periodic Stokes waves is used to prove the existence of a dispersion relation.
spatial and temporal Hamiltonian structure
ordinary differential eigenvalue problem
scientific article; zbMATH DE number 880584
scientific article