off nat;



%for all xxx let cos(xxx)**2 + sin(xxx)**2 = 1;
%for all xxx let sinh(xxx) = sqrt(cosh(xxx)**2 - 1);
%for all xxx let sinh(xxx)**2 = cosh(xxx)**2 - 1;
%for all xxx let sinh(xxx)**2 + 1 = cosh(xxx)**2;

%------- a curve in normal parametrization ---------------

kaptt:= (2*a)/cosh(a*s - (a**3)*p - cx);


KAPTT := (2*A)/COSH(A**3*P - A*S + CX)$



%------------------ mkdv test  ---------------------------


df(kaptt,p) + (3/2)*kaptt**2*df(kaptt,s) + df(kaptt,s,3);


(12*SINH(A**3*P - A*S + CX)*A**4*( - COSH(A**3*P - A*S + CX)**2 + 
SINH(A**3*P - A*S + CX)**2 + 1))/COSH(A**3*P - A*S + CX)**4$



shut kk1;