The non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources

The non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources are established and solved. Two families of quasideterminant solutions are presented for the non-Abelian two-dimensional Toda lattice with self-consistent sources. By employing periodic and quasi-periodic reductions, a matrix sine-Gordon equation with self-consistent sources is constructed for the first time, for which exact solutions in terms of quasideterminants are derived.