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-dim ensional, complex, cubic Ginzburg-Landau type. By transposing the method de veloped for one CGL3 equation, we obtain several new exact solutions expres sed by closed-form, single-valued, analytic expressions. Some of them are t he analogues of the famous amplitude hole solution of Bekki and Nozaki.