Solution 3 to problem N2t6s8f3

Equations

The following unsolved equations remain:

    2     2
0=p1  + p2

Expressions

The solution is given through the following expressions:


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9= - q5


     - p2*q5
q8=----------
       p1


q7=0


q6=0


    p2*q5
q4=-------
     p1


q3=0


q2=0


q1=0


p8=0


p7=0


p6= - p2


p5= - p1


p4=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:

 q5, 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.

 
{p1,

 q5,

 p2,

 g0022*q5 - g0025*q5 + g0029*p1 - g0032*p1,

 p5,

                                                                               2
 g0037*p1*q5 + g0038*p2*q5 - g0041*p1*q5 - g0042*p2*q5 + g0046*p1*p2 + g0047*p1

                          2
  - g0050*p1*p2 - g0051*p1 ,

 g0007*q5 - g0010*q5 + g0014*p1 - g0017*p1,

 g0069*p2 + g0070*p1 - g0073*p2 - g0074*p1,

 g0058*p1 + g0059*p2 - g0062*p1 - g0063*p2}

Relevance for the application:

The equation:


f =D f *f*p1 - D f*f *p1 + D f *f*p2 - D f*f *p2
 t  2 x         2   x       1 x         1   x

The symmetry:

    D f  *f*p1*q5 - D f *f *p1*q5 + D f  *f*p2*q5 - D f *f *p2*q5
     2 2x            2 x  x          1 2x            1 x  x
f =---------------------------------------------------------------
 s                               p1

And now in machine readable form:

The system:

df(f(1),t)=d(2,df(f(1),x))*f(1)*p1 - d(2,f(1))*df(f(1),x)*p1 + d(1,df(f(1),x))*f
(1)*p2 - d(1,f(1))*df(f(1),x)*p2$

The symmetry:

df(f(1),s)=(d(2,df(f(1),x,2))*f(1)*p1*q5 - d(2,df(f(1),x))*df(f(1),x)*p1*q5 + d(
1,df(f(1),x,2))*f(1)*p2*q5 - d(1,df(f(1),x))*df(f(1),x)*p2*q5)/p1$