Solution 3 to problem N1t6s10f3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t6s10f3

Expressions

The solution is given through the following expressions:


q7=0


q6=0


q5=0


q4=0


     1
    ---*p2*q2
     2
q3=-----------
       p1


q1=0


p3=0

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:

 q2, 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.

 
{g0021*p2 + g0022*p1,

 p1,

                                                         2
 g0008*p2*q2 + 2*g0009*p1*q2 + 2*g0011*p1*p2 + 2*g0012*p1 ,

 q2,

 g0017*p2 + 2*g0018*p1}

Relevance for the application:

The equation:


f =Df *f*p1 + Df*f *p2
 t   x            x

The symmetry:

                      1      2
    Df *Df*f*p1*q2 + ---*(Df) *f *p2*q2
      x               2         x
f =-------------------------------------
 s                  p1

And now in machine readable form:

The system:

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

The symmetry:

df(f(1),s)=(d(1,df(f(1),x))*d(1,f(1))*f(1)*p1*q2 + 1/2*d(1,f(1))**2*df(f(1),x)*
p2*q2)/p1$