Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations

Abstract

We investigate linear stability of solitary waves of a Hamiltonian system. Unlike weakly nonlinear water wave models, the physical system considered here is nonlinearly dispersive, and contains nonlinearity in its highest derivative term. This results in more detailed asymptotic analysis of the eigenvalue problem in presence of a large parameter. Combining the technique of singular perturbation with the Evans function, we show that the problem has no eigenvalues of positive real part and solitary waves of small amplitude are linearly stable.