/* Command file h_kdv.com for Korteweg-de Vries Equation */

writefile("h_kdv.out");
batchload("hir_sing.max")$  
n:3$
B(f,g):= Dxt[1,1](f,g) + Dx[4](f,g)$ 
name:KdV$
hirota(b,name,n,2,3,true,true)$

/* extra information available after the program finishes */

theta[1];
omega[3];
om[2];

factor(a[1,2]);
factor(b[1,2,3]);

f;
expression(f);

/* Setting up specific values for the wave numbers */

k[1]:1;
k[2]:3/2;
k[3]:5/4;
cst[1]:0;
cst[2]:0;
cst[3]:0;

fnumer:ev(expression(f));

/* computation of the solution u(x,t) of u_t + 6 u u_x + u_{3x} = 0 */

define(u(x,t),2*ev(diff(log(ev(expression(f))),x,2),diff));

/* 
Plotting commented out here, re-activate if your machine has plot 
capabilities 
*/

/* taken out as of here 

/* starting the plotting in 2D */

plot(u(x,0),x,-9,13);

/* starting the plotting in 3D */

plot3D(u(x,t),x,-4,4,t,-5,5);

end of taken out */

closefile();
kill(all)$
quit();

/* end of the file h_kdv.com */