Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

Abstract

We study the Veronese web equation $u_y{u}_{tx}+\lambda u_x{u}_{ty}-(\lambda +1)u_t{u}_{xy}=0$ and using its isospectral Lax pair construct two infinite series of nonlocal conservation laws. In the infinite differential coverings associated to these series, we describe the Lie algebras of the corresponding nonlocal symmetries. Finally, we construct a recursion operator and explore its action on nonlocal shadows. The operator provides a new shadow which serves as a master-symmetry.

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Cited by in corpus (2)

• Extensions of the symmetry algebra and Lax representations for the two-dimensional Euler equation
• On the algebra of nonlocal symmetries for the 4D Mart\'ınez Alonso-Shabat equation