# A Method for Constructing a Lax Pair for the Ernst Equation

C. J. Papachristou, B. Kent Harrison

Arxiv ID: 0805.1312•Last updated: 4/23/2021

A systematic construction of a Lax pair and an infinite set of conservation
laws for the Ernst equation is described. The matrix form of this equation is
rewritten as a differential ideal of gl(2,R)-valued differential forms, and its
symmetry condition is expressed as an exterior equation which is linear in the
symmetry characteristic and has the form of a conservation law. By means of a
recursive process, an infinite collection of such laws is then obtained, and
the conserved "charges" are used to derive a linear exterior equation whose
components constitute a Lax pair.

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