Notes

Chapter 4: Systems Based on Numbers

Section 9: Partial Differential Equations


[PDEs involving] different powers

The equations

D[u[t,x],t,t]==D[u[t,x],x,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]