Formula_12730

\[\begin{gathered}u(x, t) \sim-\sum_{n=1}^{m} \frac{2 k_{n}^{2}}{\cosh ^{2}\left[k_{n} x-4 k_{n}^{3} t+\Phi_{n}\right]}- \\-\sum_{n=1}^{[(N+1) / 2]} \frac{2 C^{2}}{\cosh ^{2}\left[C x-4 C^{3} t-\frac{1}{2 C} \ln t^{n+1 / 2}+\Psi_{n}\right]}+O\left(t^{-1 / 2}\right),\end{gathered}\]