Physics - the language of nature
Korteweg-deVries Equation
$$
\Large{
\begin{align}
u_t + 6\,u\,u_x + u_{xxx} &= 0\\
-c\,\phi_\xi + 6\,\phi\,\phi_\xi + \phi_{\xi\xi\xi} &= 0\\
\end{align}}
$$
$$
\Large{
\begin{align}
c &= 4\,k^2\\
k &= \pm\frac{\sqrt{c}}{2}\\
\psi (\xi) &= sech^2 (\,\xi)\\
\phi (\xi) &= 2\,k^2\,\psi (\xi)
\end{align}}
$$