The multi-field complex Bateman equation (Q1599583)

The goal of the author is to construct a Lagrangian for the complex Bateman equation and its multi-field generalization, and to find general solution of the latter. The equations presented in this paper are no worse than second order, are covariant and possess reparametrisation invariance. The author shows that among the class of explicit solutions there exists a simple generalization of the holomorphic plus anti-holomorphic function solution of the two-dimensional Laplace equation.