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We consider the four-dimensional integrable Martinez Alonso--Shabat equation,and list three integrable three-dimensional reductions thereof. We also presenta four-dimensional integrable modified Martinez Alonso--Shabat equationtogether with its Lax pair.  We also construct an infinite hierarchy of commuting nonlocal symmetries (andnot just the shadows, as it is usually the case in the literature) for theMartinez Alonso--Shabat equation.

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