the wall the chromomagnetic and chromoelectric fields are orthogonal to each other (see Fig.\[Fig:single\_kink\]). In conformity with (\[current\_cont\_sc\]) the absence of the charged current off the infinitely thin domain wall requires $$\begin{aligned}
 \partial_1\Phi|_{x_1=0}=0,\end{aligned}$$ and the eigenvalue problem on the wall takes the form $$\begin{aligned}
\label{covder_wall}
\left[- \partial_2^2 -\partial_3^2 +\breve n^2 B^2 x_3^2 + (i\partial_4-\breve n Bx_3)^2\right]\Phi=\lambda\Phi
\nonumber\end{aligned}$$ with the solution $$\begin{aligned}
\label{on_wall_sol_sc}
\Phi_k(x_2,x_3,x_4)&=&e^{ip_2x_2+ip_4x_4}e^{-\frac{|\breve n|B}{\sqrt{2}}\left(x_3-\frac{p_4}{2|\breve n|B}\right)^2}
\nonumber\\
&\times&
H_k\left[\sqrt{\sqrt{2}|\breve n|B}\left(x_3-\frac{p_4}{2|\breve n|B}\right)\right],
\nonumber\\
\lambda_k(p^2_2,p_4^2)&=&\sqrt{2}|\breve n|B(2k+1)+\frac{p_4^2}{2}+\frac{p_2^2}{2},
\nonumber\\
 &&k=0,1,2,\dots
\nonumber\end{aligned}$$ The spectrum of the eigenmodes on the wall is continuous, it depends on the momentum $p_2$ longitudinal to the chromomagnetic field and Euclidean energy $p_4$, the corresponding eigenfunctions are oscillating in $x_2$ and $x_4$. In the direction $x_3$ transverse to the chromomagnetic field the eigenfunctions are bounded and the eigenvalues display the Landau level structure. The continuation $p_4^2=-p_0^2$ leads to the dispersion relation $$p_0^2=p_2^2+\mu^2_k,\quad \mu^2_k=2\sqrt2(2k+1)|\breve n|B,\, \, k=0,1,2,\dots .$$ This can be treated as the lack of confinement - the color charged quasiparticles with masses $\mu_k$ and momentum $\mathbf{p}$ parallel to the chromomagnetic field $\mathbf{H}$ can be excited on the wall.

The case of the planar domain wall configuration (two infinite parts of the space-time separated by a three-dimentional hypersurface like in Fig.\[Fig:single\_kink\]) is 