Pseudosymmetric equations in a free monoid

In 2011, Makanin obtained the general solution of the symmetric equation $$x_1 x_2 cdots x_{n - 1} x_n = x_n x_{n - 1} cdots x_2 x_1$$ in a free monoid. In the present paper, a generalization of this result is given. Namely, we shall describe the general solution of the so-called pseudosymmetric equations in a free monoid which are obtained from the symmetric equations by transposing one (any) pair of adjacent variables.