Nonlinear solution condition

Nonlinear solution condition

The solution of nonlinear solitary wave equation can be written as
\begin{align} \phi(x) = \pm v \tanh\left[\frac{m}{ \sqrt 2} (x-x_0)\right]
\end{align}
the +ve refers kink and the minus refers anikink solution.
where $x_0$ is a constant of integration. What I dont understand from the
above equation is :
The energy density is localized near $x = x_0$ , and goes to zero
exponentially fast for $|x- x_0 | > 1/m.$ Can anyone explain me with
mathematical argument and graphical picture.
Please write if you need more information. Thanks in advance.