= Power-law nonlinear Klein-Gordon pulse
{title2=$w=C\,\operatorname{sech}^{2/(n-1)}(Bx)$}
For $f(w)=-aw+bw^n$, with $a,b>0$ and integer $n>1$, a positive localized static pulse has $C^{n-1}=a(n+1)/(2b)$ and $B=(n-1)\sqrt a/2$. Writing the same profile as $[A\cosh^2(Bx)]^{1/(1-n)}$ instead gives $A=2b/[a(n+1)]$. These are different amplitude conventions for the same solution. A <Lorentz boost> moves the pulse at <speed> $\tanh\beta$, preserves its peak height and contracts its width by $1/\cosh\beta$. Existence alone does not imply dynamical stability.
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