[PDEs involving] different powers

The equations

∂_{tt}u[t, x] ∂_{xx}u[t, x] + (1 - u[t,x]^{n})(1 + a u[t, x])

with n = 4, 6, 8, etc. appear to show similar behavior to the n = 2 equation in the main text.

[PDEs involving] different powers

The equations

∂_{tt}u[t, x] ∂_{xx}u[t, x] + (1 - u[t,x]^{n})(1 + a u[t, x])

with n = 4, 6, 8, etc. appear to show similar behavior to the n = 2 equation in the main text.

From Stephen Wolfram: *A New Kind of Science* [citation]