Nonlocal symmetries of Plebański’s second heavenly equation

Abstract

We study nonlocal symmetries of Plebański’s second heavenly equation in an infinite-dimensional covering associated to a Lax pair with a non-removable spectral parameter. We show that all local symmetries of the equation admit lifts to full-fledged nonlocal symmetries in the infinite-dimensional covering. Also, we find two new infinite hierarchies of commuting nonlocal symmetries in this covering and describe the structure of the Lie algebra of the obtained nonlocal symmetries.

Keywords:

• Plebański’s second heavenly equation
• Lax pair
• differential covering
• nonlocal symmetries

2000 Mathematics Subject Classification:

• 58H05
• 58J70
• 35A30