&=& (\partial_1-i\breve n H_2(x_1)x_3-i\breve nH_3(x_1)x_2)^2 
\nonumber\\
&& + \partial_2^2 +\partial_3^2 + (\partial_4+i\breve n Bx_3)^2 -i\partial_1B_1
\nonumber\\
\partial_\mu\breve B_\mu&=&-\breve n H^\prime_2(x_1)x_3-\breve n H^\prime_3(x_1)x_2.
\label{sing_gauge}\end{aligned}$$ The action can be written as $$\begin{aligned}
S[\Phi]&=&\int d^4x \Phi^\dagger(x)\tilde D^2\Phi(x)
\label{surf_gauge}\\
&-&i\int d^4x \Phi^\dagger(x)\breve n\Phi(x) \left[H^\prime_2(x_1)x_3+H^\prime_3(x_1)x_2\right] .  
\nonumber\end{aligned}$$ It should be noted that the integral in the second line is equal to zero if $\Phi^\dagger(x)\breve n\Phi(x)$ is an even function of $x_2$ and $x_3$.

The structure of $D^2$ in Eq.(\[covder1\]) is quite complicated. In the eigenvalue problem the variables can hardly be separated in the case of the finite width of the kink. The problem becomes much simpler and tractable in the limit of the infinitely thin domain wall $\mu\to\infty$. This limit brings discontinuity into the background field and thus creates a sharp boundary – the hyperplane of the domain wall. In such a situation one has to solve the problem in the bulk and on the wall and match the solutions according to some appropriate conditions. For our choice of the kink location there are three regions to be studied: $x_1<0$ with the self-dual field $B_\mu$, $x_1>0$ with the anti-self-dual field, and $x_1=0$ with the chromomagnetic and chromoelectric fields orthogonal to each other. Conditions imposed 