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

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 G _6,1 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.