The stability of solitary waves

The stability of finite amplitude, two‐dimensional solitary waves of permanent form in water of uniform depth with respect to two‐dimensional infinitesimal disturbances is investigated. It is numerically confirmed that the recent analytical results obtained by Saffman (submitted to J. Fluid Mech.) for the ‘‘superharmonic’’ instability of periodic waves hold also in the case of solitary waves.

[1]  B. Chen,et al.  Numerical Evidence for the Existence of New Types of Gravity Waves of Permanent Form on Deep Water , 1980 .

[2]  H. C. Longuet-Higgins,et al.  Integral properties of periodic gravity waves of finite amplitude , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  John K. Hunter,et al.  Accurate computations for steep solitary waves , 1983, Journal of Fluid Mechanics.

[4]  D. H. Peregrine,et al.  Breaking Waves on Beaches , 1983 .

[5]  Mitsuhiro Tanaka.  The Stability of Steep Gravity Waves , 1983 .

[6]  Michael Selwyn Longuet-Higgins,et al.  The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  On the stability of steep gravity waves , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  Tsunehiko Kakutani,et al.  Stability of the Burgers Shock Wave and the Korteweg-de Vries Soliton , 1970 .

[9]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .