Solution 4 to problem N1t4s8f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t4s8f1

Expressions

The solution is given through the following expressions: 

q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q5=0


q3=0


q2=0


q1=0


p4=0


p2=0


    p3*q4
q6=-------
    3*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: 
 q4, 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. 
 
{g0027*p3 + 3*g0029*p1,p1,g0034*p3 + g0036*p1}

Relevance for the application:



The equation: 



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


The symmetry: 

            2            1      3
    Df *(Df) *f*p1*q4 + ---*(Df) *f *p3*q4
      x                  3         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))**2*f(1)*p1*q4 + 1/3*d(1,f(1))**3*df(f(1),x
)*p3*q4)/p1$