The four-dimensional Martinez Alonso--Shabat equation: reductions and nonlocal symmetries

Abstract

We consider the four-dimensional integrable Martinez Alonso--Shabat equation, and list three integrable three-dimensional reductions thereof. We also present a four-dimensional integrable modified Martinez Alonso--Shabat equation together with its Lax pair. We also construct an infinite hierarchy of commuting nonlocal symmetries (and not just the shadows, as it is usually the case in the literature) for the Martinez Alonso--Shabat equation.