Hom-Lie Algebras and a Coupled Toda Equation with Indefinite Matrices

In this paper, we study one parameter deformation of a coupled Toda equation with indefinite matrices basing on the theory of Hom-Lie algebras. We construct a Miura transformation between the coupled Toda equation with indefinite matrices and the deformed coupled Toda equation with indefinite matrices. The Miura transformation can help us in deriving the solutions of the deformed coupled Toda equation with indefinite matrices.