Multiple solutions for the Schwarzian Korteweg–de Vries equation in (2 + 1) dimensions

In this paper we find new families of solutions for the (2 + 1)-dimensional integrable Schwarzian Korteweg–de Vries equation, that depend up to two arbitrary functions and a solution of a Riemann wave equation. Some of these solutions exhibit a rich dynamic, with a wide variety of qualitative behavior and structures that are exponentially localized. We have also found several families of overturning and intertwining solutions for the equation, that correspond to the nonconstant solutions of Riemann equations.