Solution
= Solution
When $\kappa=0$, the characteristics satisfy $x-at=\text{constant}$ and $u$ is constant along them. Therefore
$$
\boxed{u(t,x)=u_0(x-at)}.
$$
= Solution
When $\kappa=0$, the characteristics satisfy $x-at=\text{constant}$ and $u$ is constant along them. Therefore
$$
\boxed{u(t,x)=u_0(x-at)}.
$$