Benney, D. J. & Roskes, G. J. 1969 Wave instabilities. Stud. Appl. Maths 48 (4), 377–385.
Brinch-Nielsen, U. & Jonsson, I. G. 1986 Fourth order evolution equations and stability analysis for Stokes waves on arbitrary water depth. Wave Motion 8 (5), 455–472.
Broer, L. J. F. 1974 On the Hamiltonian theory of surface waves. Appl. Sci. Res. 29 (6), 430–446.
Caponi, E. A., Saffman, P. G. & Yuen, H. C. 1982 Instability and confined chaos in a non-linear dispersive wave system. Phys. Fluids 25 (12), 2159–2166.
Carter, J. D. 2001 Stability and existence of traveling wave solutions of the two-dimensional nonlinear Schrödinger equation and its higher-order generalizations. PhD thesis, University of Colorado at Boulder, CO.
Crawford, D. R., Saffman, P. G. & Yuen, H. C. 1980 Evolution of a random inhomogeneous field of non-linear deep-water gravity waves. Wave Motion 2, 1–16.
Davey, A. & Stewartson, K. 1974 On three-dimensional packets of surface waves. Proc. R. Soc. Lond. A 338 (1613), 101–110.
Dysthe, K. B. 1979 Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369 (1736), 105–114.
Fenton, J. D. 1985 A fifth-order Stokes theory for steady waves. J. Waterway Port Coastal Ocean Engng 111 (2), 216–234.
Gorman, R. M. 2003 The treatment of discontinuities in computing the nonlinear energy transfer for finite-depth gravity wave spectra. J. Atmos. Ocean. Technol. 20 (1), 206–216.
Gramstad, O. & Trulsen, K. 2010 Can swell increase the number of freak waves in a wind sea? J. Fluid Mech. 650, 57–79.
Janssen, P. A. E. M. 2009 On some consequences of the canonical transformation in the Hamiltonian theory of water waves. J. Fluid Mech. 637, 1–44.
Janssen, P. A. E. M. & Onorato, M. 2007 The intermediate water depth limit of the Zakharov equation and consequences for wave prediction. J. Phys. Oceanogr. 37, 2389–2400.
Krasitskii, V. P. 1994 On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech. 272, 1–20.
Krasitskii, V. P. & Kalmykov, V. A. 1993 Four-wave reduced equations for surface gravity waves. Izv. Atmos. Ocean. Phys. 29 (2), 222–228.
Kuznetsov, E. A. 1977 Solitons in a parametrically unstable plasma. Dokl. USSR 236, 575–577.
Lo, E. & Mei, C. C. 1985 A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation. J. Fluid Mech. 150, 395–416.
Luke, J. C. 1967 A variational principle for a fluid with a free surface. J. Fluid Mech. 27, 395–397.
McLean, J. W. 1982 Instabilities of finite-amplitude gravity waves on water of finite depth. J. Fluid Mech. 114, 331–341.
Miles, J. W. 1977 On Hamilton's principle for surface waves. J. Fluid Mech. 83, 153–158.
Peregrine, D. H. 1983 Water waves, nonlinear Schrödinger equations and their solutions. J. Austral. Math. Soc. B 25, 16–43.
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193–217.
Segur, H., Henderson, D. M. & L., Hammack, J. 2005 Can the Benjamin–Feir instability spawn a rogue wave? In Proceedings of the 14th 'Aha Huliko'a Hawaiian Winter Workshop, Honolulu, Hawaii (ed. Müller, P. & Henderson, D.), pp. 43–57. SOEST Special Publication.
Stiassnie, M. 1984 Note on the modified nonlinear Schrödinger-equation for deep-water waves. Wave Motion 6 (4), 431–433.
Stiassnie, M. & Gramstad, O. 2009 On Zakharov's kernel and the interaction of non-collinear wavetrains in finite water depth. J. Fluid Mech. 639, 433–442.
Stiassnie, M. & Shemer, L. 1984 On modifications of the Zakharov equation for surface gravity waves. J. Fluid Mech. 143, 47–67.
Sulem, C. & Sulem, P. L. 1999 The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse, Applied Mathematical Sciences, vol. 139. Springer.
Trulsen, K. & Dysthe, K. B. 1996 A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24 (3), 281–289.
Trulsen, K. & Dysthe, K. B. 1997 Frequency downshift in three-dimensional wave trains in a deep basin. J. Fluid Mech. 352, 359–373.
Trulsen, K., Kliakhandler, I., Dysthe, K. B. & Velarde, M. G. 2000 On weakly nonlinear modulation of waves on deep water. Phys. Fluids 12 (10), 2432–2437.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Yuen, H. C. & Lake, B. M. 1982 Nonlinear dynamics of deep-water gravity waves. Adv. Appl. Mech. 22, 67–229.
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190–194.
Zakharov, V. E. 1999 Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid. Eur. J. Mech. B 18 (3), 327–344.
Zakharov, V. E. & Dyachenko, A. I. 2010 About shape of giant breather. Eur. J. Mech. B 29 (2), 127–131.
Zakharov, V. E. & Shabat, A. B. 1972 Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62–69.