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.

7 pages, LaTeX, major revision (in particular, the section on the modified Alonso--Shabat equation was added)

References in corpus (3)

• The four-dimensional Martinez Alonso - Shabat equation: differential coverings and recursion operators
• Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations
• Linearly degenerate PDEs and quadratic line complexes

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• A Bäcklund transformation between 4D Mart\'ınez Alonso -- Shabat and Ferapontov -- Khusnutdinova equations
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• On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems
• On the algebra of nonlocal symmetries for the 4D Mart\'ınez Alonso-Shabat equation
• Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws