Solution 10 to problem N1t8s12f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s12f1

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


q27=0


q26=5*q3


q25=0


q24=0


q23=0


q22=0


q21=0


q20=4*q6


q19= - 11*q3 + 4*q7


q18=0


q17=0


q16= - 3*q3


q15=0


q14= - 3*q6


            3
q13=3*q3 - ---*q7
            2


        3
q12= - ---*q9
        5


q11=0


q10=3*q6


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


q5=0


q4=0


q2=0


q1=0


p13=0


p12=0


p11=0


p10=0


p9=0


p8=0


p7=0


p5=0


p4= - p6


p3=0


p2=0


p1=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:

 q9, q7, q6, q3, p6

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.

 
{p4,

 p6,

 50*g0013*q3 + 40*g0019*q6 - 110*g0020*q3 + 40*g0020*q7 - 30*g0023*q3

  - 30*g0025*q6 + 30*g0026*q3 - 15*g0026*q7 - 6*g0027*q9 + 30*g0029*q6

  + 10*g0030*q9 - 10*g0031*q3 + 5*g0031*q7 + 10*g0032*q7 + 10*g0033*q6

  + 10*g0036*q3 + 10*g0045*p6 - 10*g0047*p6,

 50*g0060*q3 + 40*g0066*q6 - 110*g0067*q3 + 40*g0067*q7 - 30*g0070*q3

  - 30*g0072*q6 + 30*g0073*q3 - 15*g0073*q7 - 6*g0074*q9 + 30*g0076*q6

  + 10*g0077*q9 - 10*g0078*q3 + 5*g0078*q7 + 10*g0079*q7 + 10*g0080*q6

  + 10*g0083*q3}

Relevance for the application:

The equation:


              2            3
f = - Df *(Df) *f*p6 + (Df) *f *p6
 t      x                     x

The symmetry:

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

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

    3       2                    4                  3
 - ---*(Df ) *Df*f *q7 + Df *(Df) *f*q9 - 3*Df *(Df) *f *q6 - 11*Df *f  *f *f*q3
    2     x       x        x                  x        x           x  2x  x

                        3      5               2
 + 4*Df *f  *f *f*q7 - ---*(Df) *f *q9 + 4*(Df) *f  *f *f*q6 + 5*Df*f  *f *f*q3
       x  2x  x         5         x               2x  x              3x  x

And now in machine readable form:

The system:

df(f(1),t)= - d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p6 + d(1,f(1))**3*df(f(1),x)*p6$

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 - 3*d(1,df(f(1)
,x,2))*d(1,f(1))**2*df(f(1),x)*q3 - d(1,df(f(1),x))**3*f(1)*q3 + 1/2*d(1,df(f(1)
,x))**3*f(1)*q7 + 3*d(1,df(f(1),x))**2*d(1,f(1))**2*f(1)*q6 + 3*d(1,df(f(1),x))
**2*d(1,f(1))*df(f(1),x)*q3 - 3/2*d(1,df(f(1),x))**2*d(1,f(1))*df(f(1),x)*q7 + d
(1,df(f(1),x))*d(1,f(1))**4*f(1)*q9 - 3*d(1,df(f(1),x))*d(1,f(1))**3*df(f(1),x)*
q6 - 11*d(1,df(f(1),x))*df(f(1),x,2)*df(f(1),x)*f(1)*q3 + 4*d(1,df(f(1),x))*df(f
(1),x,2)*df(f(1),x)*f(1)*q7 - 3/5*d(1,f(1))**5*df(f(1),x)*q9 + 4*d(1,f(1))**2*df
(f(1),x,2)*df(f(1),x)*f(1)*q6 + 5*d(1,f(1))*df(f(1),x,3)*df(f(1),x)*f(1)*q3$