k1:1; k2:2; d1:0; d2:0;
b1:4*k1^3; b2:4*k2^3;
e1:k1*x-b1*t+d1;
e2:k2*x-b2*t+d2;

b:matrix([1+exp(2*e1)/(2*k1),exp(e1+e2)/(k1+k2)],
         [exp(e2+e1)/(k2+k1),1+exp(2*e2)/(2*k2)]);
f:determinant(b);
u:2*diff(log(f),x,2);
u:ratsimp(u);
plot3d(u,[t,-5,5],[x,-30,30],[grid,50,50]);
a:diff(u,t)+6*u*diff(u,x)+diff(u,x,3);
b:ratsimp(a);