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A simple equation is derived for the nonlinear evolution of a front (a potential-vorticity discontinuity) in the rotating shallow-water equations, assuming weak along-front variations relative to the internal radius of deformation. This equation can be transformed into the modified Korteweg–de Vries equation, which is integrable and possesses exact, time-dependent solutions.
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Nycander et al. (1993) studied this question.
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