Formula_1104

\[\begin{gathered}u(x, t)=(2|t|)^{-3 / 2} C(-s,-x / r) e^{i r^{2} / 4 t}+O\left(|t|^{-2}\right), \quad t \rightarrow-\infty, \\u(x, t)=(2 t)^{-3 / 2}\left(C(s, x / r)+\frac{i s}{2 \pi} f(s, x / r) \int_{S^{2}} C(k, \omega) d \omega\right) e^{i r^{2} / 4 t}+ \\+O\left(t^{-2}\right), \quad t \rightarrow+\infty .\end{gathered}\]