Solution 3 to problem N1t4s10f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t4s10f1

Expressions

The solution is given through the following expressions:


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q7=0


q6=0


q4=0


q3=0


q2=0


q1=0


p4=0


p2=0


    p3*q5
q8=-------
    4*p1

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:

 q5, p1, 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.

 
{g0041*p3 + 4*g0044*p1,p1,g0050*p3 + g0052*p1}

Relevance for the application:

The equation:


f =Df *f*p1 + Df*f *p3
 t   x            x

The symmetry:

            3            1      4
    Df *(Df) *f*p1*q5 + ---*(Df) *f *p3*q5
      x                  4         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)*p3$

The symmetry:

df(f(1),s)=(d(1,df(f(1),x))*d(1,f(1))**3*f(1)*p1*q5 + 1/4*d(1,f(1))**4*df(f(1),x
)*p3*q5)/p1$