Solution 1 to problem N1t8s11f2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s11f2

Expressions

The solution is given through the following expressions:


q7=0


q6=0


q5=0


q4=0


q1=0


p3=0


    3*p1*q3
q2=---------
     2*p2

Parameters

Apart from the condition that they must not vanish to give a non-trivial solution and a non-singular solution with non-vanishing denominators, the following parameters are free:

 q3, p2, p1

Inequalities

In the following not identically vanishing expressions are shown. Any auxiliary variables g00?? are used to express that at least one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3 means that either p4 or p3 or both are non-vanishing.

 
{g0013*p2 + g0014*p1,2*g0009*p2 + 3*g0010*p1}

Relevance for the application:

The equation:


                     2
f =Df *Df*f*p1 + (Df) *f *p2
 t   x                  x

The symmetry:

     3          2               3
    ---*Df *(Df) *f*p1*q3 + (Df) *f *p2*q3
     2    x                        x
f =----------------------------------------
 s                    p2

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))*d(1,f(1))*f(1)*p1 + d(1,f(1))**2*df(f(1),x)*p2$

The symmetry:

df(f(1),s)=(3/2*d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p1*q3 + d(1,f(1))**3*df(f(1),x
)*p2*q3)/p2$