TY - JOUR
T1 - Hamiltonian structure and linear stability of solitary waves of the Green-Naghdi equations
AU - Li, Yi A.
N1 - Publisher Copyright:
Copyright © 2002 by Yi A Li.
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
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U2 - 10.2991/jnmp.2002.9.s1.9
DO - 10.2991/jnmp.2002.9.s1.9
M3 - Article
AN - SCOPUS:52349121353
SN - 1402-9251
VL - 9
SP - 99
EP - 105
JO - Journal of Nonlinear Mathematical Physics
JF - Journal of Nonlinear Mathematical Physics
ER -