Volume 9, Issue Supplement 1, February 2002, Pages 99 - 105
Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations
Yi A. Li
Yi A. Li
Received 30 May 2001, Revised 8 July 2001, Accepted 15 July 2001, Available Online 1 February 2002.
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- 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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Cite this article
TY - JOUR AU - Yi A. Li PY - 2002 DA - 2002/02 TI - Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations JO - Journal of Nonlinear Mathematical Physics SP - 99 EP - 105 VL - 9 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.s1.9 DO - https://doi.org/10.2991/jnmp.2002.9.s1.9 ID - Li2002 ER -