Problem: Find a traveling-wave solution to $u_t = -u_{xx} - 2 u u_x^2/(1 - u^2)$, such that $u \rightarrow 0$ as $t \rightarrow \infty$, $u \rightarrow 1$ as $t \rightarrow -\infty$, $u(0,0) - 0.76159 < 0.01$, and $u_x(0,0) - 0.41997 < 0.01$. Please place your final solution in a $\boxed{}$ LaTeX Environment. The only remaining parameters in your final solution should be $x$ and $t$; do not define additional parameters or constants.
Solution: $$\boxed{u(x,t) = \tanh(e^{x - t})}$$