we can determine the structure of the domain wall by taking $\epsilon_1 = 0$. With this, and defining $\theta^\prime \equiv 2 \theta$, we get the following equation of motion for $\theta^\prime$, $$\Box \theta^\prime + \epsilon_2 \sin \theta^\prime = 0 \, .$$ This is the familiar sine-Gordan equation which is known to have the domain-wall solutions [@avae] $$\theta^\prime(z) \,=\, 4 \tan^{-1} \left[ \exp\left({\sqrt
\epsilon_2} z \right)\right] \, ,$$ where the $z$ axis is normal to the wall. The thickness of the wall is $\delta \simeq \epsilon_2^{-1/2}$. Thus the surface energy density $\rho_S$ of the wall is of the order $$\rho_S \simeq \epsilon_2 v^2 \delta = v^2 {\sqrt \epsilon_2} \, .$$

When $\epsilon_1$ is nonzero then, even though domain walls still form, they are not stable any more. \[It is simple to check that domain walls always form as long as $\epsilon_1 <
f_{\pi} \epsilon_2$, which is just the condition that there be a local minimum at $\theta = \pi$.\] Instability of the wall arises because now one minimum ($\theta = 0$) is energetically preferred over the other ($\theta = \pi$) so the region corresponding to $\theta = \pi$ shrinks while the region corresponding to $\theta = 0$ expands. These unstable domain 