English

A Method for Constructing a Lax Pair for the Ernst Equation

Mathematical Physics 2024-08-29 v2 math.MP

Abstract

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.

Cite

@article{arxiv.0805.1312,
  title  = {A Method for Constructing a Lax Pair for the Ernst Equation},
  author = {C. J. Papachristou and B. Kent Harrison},
  journal= {arXiv preprint arXiv:0805.1312},
  year   = {2024}
}

Comments

12 pages; minor corrections

R2 v1 2026-06-21T10:38:53.539Z