Abstract
We investigate the eigenvalue problem obtained from linearizing the Green-Naghdi equations about solitary wave solutions. Unlike weakly nonlinear water wave models, the physical system considered here has nonlinearity in its highest derivative term. This results in more detailed asymptotic analysis of the eigenvalue problem in the presence of a large parameter. Combining the technique of singular perturbation with the Evans function, we show that for solitary waves of small amplitude, the problem has no eigenvalues of positive real part and the Evans function is nonvanishing everywhere except the origin. This fact then leads to the linear stability of these solitary waves.
Original language | English |
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Pages (from-to) | 501-536 |
Number of pages | 36 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 54 |
Issue number | 5 |
DOIs | |
State | Published - May 2001 |