and refining the spectrum and eigenmodes of the color charged scalar, spinor and vector fields in the background of a domain wall. In particular the spectrum of quasiparticles inside the thick domain wall junction is evaluated.

It is shown that the standard methods of the sine-Gordon model [@Vachaspati] allow one to generate various domain wall networks. The eigenvalues and eigenfunctions are found for the Laplace operator in the background of a single infinitely thin domain wall. In this case, the eigenvalue problem has to be solved separately in the bulk of $R^4$ and on the 3-dimensional hyperplane of the wall. The continuity of the charge current through the wall is required together with the square integrability of the bulk eigenfunctions. For the infinitely thin wall the bulk eigenfunction possesses the purely discrete spectrum which coincides with the spectrum for the case of a homogeneous (anti-)self-dual field without a kink defect. The eigenfunctions differ in a certain way but have the same harmonic oscillator type as the ones in the absence of the kink defect. These modes describe confined color charged fields. The eigenfunctions localized on the wall have continuous spectrum with the dispersion relation of charged quasi-particles. This confirms qualitative 