Analytic expressions of hydrothermal waves

When subjected to a horizontal temperature difference, a fluid layer with a free surface becomes unstable and hydrothermal waves develop in the bulk. Such a system is modelled by two coupled amplitude equations of the one-dimensional, complex, cubic Ginzburg-Landau type. By transposing the method developed for one CGL3 equation, we obtain several new exact solutions expressed by closed-form, single-valued, analytic expressions. Some of them are the analogues of the famous amplitude hole solution of Bekki and Nozaki.