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A Lagrangian for water waves
1.G. G. Stokes, “On the theory of oscillatory waves,” Trans. Cambridge Philos. Soc. 8, 441 (1847).
2.G. G. Stokes, “Supplement to a paper on the theory of oscillatory waves,” Mathematical and Physical Papers (Cambridge University Press, Cambridge, 1880), Vol. 1, pp. 225–228.
3.M. S. Longuet-Higgins, “Some new relations between Stokes’s coeffi-cients in the theory of gravity waves,” J. Inst. Math. Appl. 22, 261 (1978).
4.P. G. Saffman, “Long wavelength bifurcation of gravity waves on deep water,” J. Fluid Mech. 101, 567 (1980).
5.J. A. Zufiria, “Non-symmetric gravity waves on water of infinite depth,” J. Fluid Mech. 181, 17 (1987).
6.V. E. Zakharov, “Stability of periodic waves of finite amplitude on the surface of deep fluid,” J. Appl. Mech. Tech. Phys. 2, 190 (1968).
7.The function L in the variational principle considered in the text [G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1973) [see formula (13.17)] is not strictly a Lagrangian, as it is not expressed in terms of generalized coordinates, it does not define the canonical Lagrange equations, and the Legendre transform is not applicable.
8.M. S. Longuet-Higgins, “Bifurcation in gravity waves,” J. Fluid Mech. 151, 457 (1985).
9.D. I. Meiron, S. A. Orszag, and M. Israeli, “Applications of numerical conformal mapping,” J. Comput. Phys. 40, 345 (1981).
10.J. A. Simmen and P. G. Saffman, “Steady deep water waves on a linear shear current,” Stud. Appl. Math. 73, 35 (1985).
11.A. I. Dyachenko, E. A. Kuznetsov, M. D. Spector, and V. E. Zakharov, “Canonical formalism and conformal mapping for the free-surface hydrodynamics,” to appear in Phys. Lett. A.
12.A. I. Dyachenko, Y. V. Lvov, and V. E. Zakharov, “Five-wave interaction on the surface of deep fluid,” Physica D 87, 233 (1995).
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