Internal solitary waves

Internal solitary waves are an ubiquitous feature of the coastal ocean and atmospheric boundary layer. We will review the use of the variable coefficient Korteweg de Vries equation, and the extended Korteweg de-Vries equation (that is, with an extra cubic nonlinear term), to model these waves. We will describe both the adiabatic theories for slowly-varying solitary waves, and the results from numerical simulations. Particular emphasis will be placed on the consequences when the coefficients of either of the nonlinear terms undergoes a sign change, which may lead to a radical and non-adiabatic change of the wave-form.