  In this paper, we study the dynamics of the charged particle interacting with
the non-null electromagnetic knot wave background. We analyse the classical
system in the Hamilton-Jacobi formalism and find the action, the linear
momentum and the trajectory of the particle. Also, we calculate the effective
mass and the emitted radiation along the knot wave. Next, we quantize the
system in the classical strong knot wave background by using the strong-field
QED canonical formalism. We explicitly construct the Furry picture and
calculate the Volkov solutions of the Dirac equation. As an application, we
discuss the one-photon Compton effect where we determine the general form of
the $S$-matrix. Also, we discuss in details the first partial amplitudes in the
transition matrix in two simple backgrounds and show that there is a pair of
states for which these amplitudes are identical.
