The Whitham equation was proposed as a model for surface water waves that combines the quadratic flux nonlinearity
Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
Abstract. Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, Earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable depth, i.e., the rotating Gardner model. These results are also compared to analysis in the Korteweg–de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.
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 Award ID(s):
 1736698
 NSFPAR ID:
 10395704
 Date Published:
 Journal Name:
 Nonlinear Processes in Geophysics
 Volume:
 29
 Issue:
 2
 ISSN:
 16077946
 Page Range / eLocation ID:
 207 to 218
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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