Solution 1 to problem N1f1b0o36w3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o36w3

Expressions

The solution is given through the following expressions: 

q12=0


        2
q11= - ---*q3
        7


q10=0


q9=0


q8=0


       2
q7= - ---*q3
       7


       3
q6= - ---*q3
       7


q5=0


q4=0


    3
q2=---*q3
    7


q1=0


p3=0


p2= - 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: 
 q3, 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. 
 
{q3,

 p1,

 p2,

 2*g0003*q3 + 2*g0007*q3 + 3*g0008*q3 - 7*g0011*q3 - 3*g0012*q3 + 7*g0014*p1

  - 7*g0015*p1,

 q6}

Relevance for the application:



The equation: 

f =Df *f*p1 - Df*f *p1
 t   x            x


The symmetry: 

                   3       2         3                  2      2
f =Df  *Df*f*q3 + ---*(Df ) *f*q3 - ---*Df *Df*f *q3 - ---*(Df) *f  *q3
 s   2x            7     x           7    x     x       7         2x

    2
 - ---*f  *f *f*q3
    7   2x  x


And now in machine readable form: 

The equation: 
df(f(1),t)=d(1,df(f(1),x))*f(1)*p1 - d(1,f(1))*df(f(1),x)*p1$


The symmetry: 

df(f(1),s)=d(1,df(f(1),x,2))*d(1,f(1))*f(1)*q3 + 3/7*d(1,df(f(1),x))**2*f(1)*q3 
- 3/7*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q3 - 2/7*d(1,f(1))**2*df(f(1),x,2)*q3
 - 2/7*df(f(1),x,2)*df(f(1),x)*f(1)*q3$