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 modelized 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, singlevalued, analytic expressions. Some of them are the analogue of the famous amplitude hole solution of Bekki and Nozaki.