Solution 8 to problem N1t10s14f3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t10s14f3

Expressions

The solution is given through the following expressions:


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q3=0


q2=0


q1=0


p7=0


p6=0


p5=0


p4=0


p1=0


    2*p3*q4
q5=---------
     3*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:

 q4, p2, p3

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.

 
{2*g0037*p3 + 3*g0038*p2,p2,g0046*p3 + g0047*p2}

Relevance for the application:

The equation:


                     2
f =Df *Df*f*p2 + (Df) *f *p3
 t   x                  x

The symmetry:

            2            2      3
    Df *(Df) *f*p2*q4 + ---*(Df) *f *p3*q4
      x                  3         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)*p2 + d(1,f(1))**2*df(f(1),x)*p3$

The symmetry:

df(f(1),s)=(d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p2*q4 + 2/3*d(1,f(1))**3*df(f(1),x
)*p3*q4)/p2$