Articles | Volume 24, issue 2
Research article
06 Jun 2017
Research article |  | 06 Jun 2017

Lagrange form of the nonlinear Schrödinger equation for low-vorticity waves in deep water

Anatoly Abrashkin and Efim Pelinovsky

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Cited articles

Abrashkin, A. A. and Yakubovich, E. I.: Vortex Dynamics in the Lagrangian Description, Fizmatlit, Moscow, 2006 (in Russian).
Abrashkin, A. A. and Zen'kovich, D. A.: Vortical stationary waves on shear flow, Izvestiya, Atmos. Ocean. Phys., 26, 35–45, 1990.
Akhmediev, N. N., Eleonskii, V. M., and Kulagin, N. E.: Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions, J. Exp. Theor. Phys., 89, 1542–1551, 1985.
Baumstein, A. I.: Modulation of gravity waves with shear in water, Stud. Appl. Math., 100, 365–390, 1998.
Bennett, A.: Lagrangian Fluid Dynamics, Cambridge University Press, Cambridge, 2006.
Short summary
The nonlinear Schrödinger equation describing weakly rotational wave packets in a fluid in the Lagrangian coordinates is derived. Rogue effects are possible in low-vorticity waves, and the effect of vorticity is manifested in a shift of the wave number in the carrier wave. Special attention is paid to Gouyon and Gerstner waves. It is shown that this equation in the Eulerian variables can be obtained from the Lagrangian solution with an ordinary change in the horizontal coordinates.