Solution 4 to problem N2t6s8f3

Remaining equations | Expressions | Parameters | Inequalities | Relevance | Back to problem N2t6s8f3

Equations

The following unsolved equations remain: 
    2     2
0=p3  + p4

Expressions

The solution is given through the following expressions: 

q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


    p3*q8
q9=-------
     p4


        1    2
     - ---*p3 *q8
        3
q7=---------------
           2
         p4


        1
     - ---*p3*q8
        3
q6=--------------
         p4


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6= - p3


p5=p4


p2=2*p3


p1= - 2*p4

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: 
 q8, p4, 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. 
 
{p5,

                            2                                 3             3
 3*g0007*p3*p4*q8 - g0008*p3 *q8 - g0009*p3*p4*q8 + 3*g0014*p4  + 3*g0015*p4

                 2             3
  + 3*g0016*p3*p4  - 6*g0017*p4 ,

 p4,

 p3,

 q8,

 p2,

 p1,

                           2           2
 3*g0058*p3*p4 + 3*g0059*p4  - g0060*p3  - g0061*p3*p4,

 p6,

           2              2                                    2             3
 3*g0022*p4 *q8 - g0023*p3 *q8 - g0024*p3*p4*q8 - 3*g0029*p3*p4  + 3*g0030*p4

                 2                2
  + 3*g0031*p3*p4  + 6*g0032*p3*p4 ,

                              2              2
 3*g0037*p3*p4*q8 + 3*g0038*p4 *q8 - g0039*p3 *q8 - g0040*p3*p4*q8

                 2             3             3                2                2
  - 3*g0046*p3*p4  + 3*g0047*p4  + 3*g0048*p4  + 3*g0049*p3*p4  + 6*g0050*p3*p4

              3
  - 6*g0051*p4 ,

 g0069*p3 - g0070*p4 - g0071*p4 - g0072*p3 - 2*g0073*p3 + 2*g0074*p4}

Relevance for the application:



The equation: 



f = - 2*D f *f*p4 + D f*D D f*p3 + D f*f *p4 + D D f*D f*p4 + 2*D f *f*p3
 t       2 x         2   1 2        2   x       1 2   1          1 x

 - D f*f *p3
    1   x


The symmetry: 

        1               2                          1
f =( - ---*D f *D D f*p3 *q8 + D f *f *p3*p4*q8 - ---*D D f*D f *p3*p4*q8
 s      3   2 x  1 2            2 x  x             3   1 2   1 x

                 2       2
     + D f *f *p4 *q8)/p4
        1 x  x


And now in machine readable form: 

The system: 

df(f(1),t)= - 2*d(2,df(f(1),x))*f(1)*p4 + d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1)
)*df(f(1),x)*p4 + d(1,d(2,f(1)))*d(1,f(1))*p4 + 2*d(1,df(f(1),x))*f(1)*p3 - d(1,
f(1))*df(f(1),x)*p3$


The symmetry: 

df(f(1),s)=( - 1/3*d(2,df(f(1),x))*d(1,d(2,f(1)))*p3**2*q8 + d(2,df(f(1),x))*df(
f(1),x)*p3*p4*q8 - 1/3*d(1,d(2,f(1)))*d(1,df(f(1),x))*p3*p4*q8 + d(1,df(f(1),x))
*df(f(1),x)*p4**2*q8)/p4**2$