New solutions are derived for the two-dimensional Toda lattice and matrix sine-Gordon equation, highlighting novel self-consistent sources.
The non-Abelian two-dimensional Toda lattice (2DTL) and matrix sine-Gordon (sG) equation with self-consistent sources are established and solved. Two families of quasi-determinant solutions are presented for the 2DTL with self-consistent sources. By employing periodic and quasi-periodic reductions, a matrix sG equation with self-consistent sources is constructed for the first time, for which exact solutions in terms of quasi-determinants are derived.
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Cui et al. (2025) studied this question.
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