Coupled systems of nonlinear wave equations and finite-dimensional lie algebras II: A nonlinear system arising from the group G 6.1 and its exact integration

Abstract

In the first paper of this series a correspondence was established between coupled systems of two-dimensional nonlinear wave equations and the six-dimensional simply transitive Lie algebras. In the present paper we make use of this result to construct a Darboux integrable and exactly integrable nonlinear system associated with the six-parameter nilpotent Lie group G6,1 and we give its exact general solution in terms of four arbitrary functions. The procedure is shown to be an exact linearization of the nonlinear problem.