Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws
arXiv:1901.07527 · doi:10.1007/s00023-019-00816-0
Abstract
We present an infinite hierarchy of nonlocal conservation laws for the Przanowski equation, an integrable second-order PDE locally equivalent to anti-self-dual vacuum Einstein equations with nonzero cosmological constant. The hierarchy in question is constructed using a nonisospectral Lax pair for the equation under study. As a byproduct, we obtain an infinite-dimensional differential covering over the Przanowski equation.
11 pages, no figures, expanded and revised version