Solution 2 to problem N1t4s12f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t4s12f1

Expressions

The solution is given through the following expressions: 

q35=0


q34=0


q33=0


q32=0


q31=0


q30=0


q29=0


q28=0


        1        1        1
q27= - ---*q3 + ---*q7 - ---*q8
        3        6        3


     3
q26=---*q7 - 3*q8
     2


q25=0


q24=0


q23=0


q22=0


q21=0


q20=2*q6


               1
q19= - 2*q3 + ---*q7 + 3*q8
               2


q18=0


q17=0


        1
q16= - ---*q7 + q8
        2


q15=0


q14= - q6


q13= - q8


        1
q12= - ---*q9
        5


q11=0


q10=3*q6


q5=0


q4=0


q2=0


q1=0


p4=0


p2=0


p1= - p3

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: 
 q9, q8, q7, q6, q3, 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. 
 
{p3,

 p1,

 10*g0012*q3 - 5*g0012*q7 + 10*g0012*q8 - 45*g0013*q7 + 90*g0013*q8

  - 60*g0019*q6 + 60*g0020*q3 - 15*g0020*q7 - 90*g0020*q8 + 15*g0023*q7

  - 30*g0023*q8 + 30*g0025*q6 + 30*g0026*q8 + 6*g0027*q9 - 90*g0029*q6

  - 30*g0030*q9 - 30*g0031*q8 - 30*g0032*q7 - 30*g0033*q6 - 30*g0036*q3

  - 30*g0039*p3 + 30*g0041*p3,

 10*g0050*q3 - 5*g0050*q7 + 10*g0050*q8 - 45*g0051*q7 + 90*g0051*q8

  - 60*g0057*q6 + 60*g0058*q3 - 15*g0058*q7 - 90*g0058*q8 + 15*g0061*q7

  - 30*g0061*q8 + 30*g0063*q6 + 30*g0064*q8 + 6*g0065*q9 - 90*g0067*q6

  - 30*g0068*q9 - 30*g0069*q8 - 30*g0070*q7 - 30*g0071*q6 - 30*g0074*q3}

Relevance for the application:



The equation: 



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


The symmetry: 

            2                                    3         1           2
f =Df  *(Df) *f*q3 + Df  *Df *Df*f*q7 + Df  *(Df) *f*q6 - ---*Df  *(Df) *f *q7
 s   3x                2x   x             2x               2    2x        x

            2              3               2     2             2
 + Df  *(Df) *f *q8 + (Df ) *f*q8 + 3*(Df ) *(Df) *f*q6 - (Df ) *Df*f *q8
     2x        x         x               x                   x       x

           4                3                              1
 + Df *(Df) *f*q9 - Df *(Df) *f *q6 - 2*Df *f  *f *f*q3 + ---*Df *f  *f *f*q7
     x                x        x          x  2x  x         2    x  2x  x

                        1      5          1      3           1      3
 + 3*Df *f  *f *f*q8 - ---*(Df) *f *q9 - ---*(Df) *f  *q3 + ---*(Df) *f  *q7
       x  2x  x         5         x       3         3x       6         3x

    1      3                2                3
 - ---*(Df) *f  *q8 + 2*(Df) *f  *f *f*q6 + ---*Df*f  *f *f*q7
    3         3x               2x  x         2      3x  x

 - 3*Df*f  *f *f*q8
         3x  x


And now in machine readable form: 

The system: 

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


The symmetry: 

df(f(1),s)=d(1,df(f(1),x,3))*d(1,f(1))**2*f(1)*q3 + d(1,df(f(1),x,2))*d(1,df(f(1
),x))*d(1,f(1))*f(1)*q7 + d(1,df(f(1),x,2))*d(1,f(1))**3*f(1)*q6 - 1/2*d(1,df(f(
1),x,2))*d(1,f(1))**2*df(f(1),x)*q7 + d(1,df(f(1),x,2))*d(1,f(1))**2*df(f(1),x)*
q8 + d(1,df(f(1),x))**3*f(1)*q8 + 3*d(1,df(f(1),x))**2*d(1,f(1))**2*f(1)*q6 - d(
1,df(f(1),x))**2*d(1,f(1))*df(f(1),x)*q8 + d(1,df(f(1),x))*d(1,f(1))**4*f(1)*q9 
- d(1,df(f(1),x))*d(1,f(1))**3*df(f(1),x)*q6 - 2*d(1,df(f(1),x))*df(f(1),x,2)*df
(f(1),x)*f(1)*q3 + 1/2*d(1,df(f(1),x))*df(f(1),x,2)*df(f(1),x)*f(1)*q7 + 3*d(1,
df(f(1),x))*df(f(1),x,2)*df(f(1),x)*f(1)*q8 - 1/5*d(1,f(1))**5*df(f(1),x)*q9 - 1
/3*d(1,f(1))**3*df(f(1),x,3)*q3 + 1/6*d(1,f(1))**3*df(f(1),x,3)*q7 - 1/3*d(1,f(1
))**3*df(f(1),x,3)*q8 + 2*d(1,f(1))**2*df(f(1),x,2)*df(f(1),x)*f(1)*q6 + 3/2*d(1
,f(1))*df(f(1),x,3)*df(f(1),x)*f(1)*q7 - 3*d(1,f(1))*df(f(1),x,3)*df(f(1),x)*f(1
)*q8$