On formal solutions to matrix version of a reduced Kac–van Moerbeke equation Original Research Article

In this paper we construct a family of formal power series––logarithmic solutions to a matrix non-linear differential-difference equation of both advanced and retarded type. In the scalar case, this equation represents a self-similar reduction of Kac–van Moerbeke equation. An interesting type of “non-resonance” conditions that guarantee the existence of formal power series––logarithmic solutions was determined.