Nonlinear Internal Waves in the Ocean Stratified
in Density and Current

E. N. Pelinovskii*^, **, O. E. Polukhina*^, **, and K. Lamb***

*Institute of Applied Physics,
Russian Academy of Sciences, Nizhni Novgorod, Russia
**Nizhni Novgorod Technical University, Nizhni Novgorod, Russia
***Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada

Received August 24, 1999; in final form, March 15, 2000

Abstract—A nonlinear theory of long internal waves in the ocean stratified in density and current was devel-
oped. A nonlinear evolutionary equation of the type of the generalized Korteweg–de Vries equation with an
accuracy of the third order of the perturbation theory was obtained in the framework of asymptotic methods.
The procedures of decomposition and calculation of all coefficients of the evolutionary equation were auto-
mated with the help of the Maple package of symbolical calculations. Internal waves in a two-layer ocean (the
upper layer moves at a constant speed) and in a three-layer ocean with a background current in the intermediate
layer were considered as examples. The properties of large-amplitude solitons in a stratified ocean were inves-
tigated. The contribution of high-order terms with respect to nonlinearity and dispersion to the soliton structure
was estimated.

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