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In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.
D. Henry and R.Ivanov, One-dimensional weakly nonlinear model equations for Rossby waves, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Volume 34, Number 8, August 2014 pp. 3025--3034, D.O.I. 10.3934/dcds.2014.34.3025