k:1;
c:4*k^2;
d:0;
f:1+exp(-2*k*(x-c*t+d));
u:2*diff(log(f),x,2);
u:ratsimp(u);
plot3d(u,[t,0,5],[x,-30,30],[grid,50,50]);
a:diff(u,t)+6*u*diff(u,x)+diff(u,x,3);
b:ratsimp(a);