[PDEs involving] different powers

The equations

∂_ttu[t, x]  ∂_xxu[t, x] + (1 - u[t,x]ⁿ)(1 + a u[t, x])

\!\(\*SubscriptBox[\(\[PartialD]\),\(tt\)]\)u[t,x]==\!\(\*SubscriptBox[\(\[PartialD]\),\(xx\)]\)u[t,x]+(1-\!\(\*SuperscriptBox[\(u[t,x]\),\(n\)]\))(1+a u[t,x])

with n = 4

n = 4, 6, 8, etc. appear to show similar behavior to the n = 2

✖

n = 2 equation in the main text.