Stability of water waves

The Royal Society - Tập 406 Số 1830 - Trang 115-125 - 1986
Robert S. MacKay1, P. G. Saffman2
1Mathematics Institute, University of Warwick, Coventry, CV4 7AL, U.K.
2Applied Mathematics, California Institute of Technology, Pasadena, California 91125, U.S.A.

Tóm tắt

We apply some general results for Hamiltonian systems, depending on the notion of signature of eigenvalues, to determine the circumstances under which collisions of imaginary eigenvalue for the linearized problem about a travelling water wave of permanent form are avoided or lead to loss of stability, up to non-degeneracy assumptions. A new superharmonic instability is predicted and verified.

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