Solution 5 to problem N1f1b0o36w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o36w1

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=4*q3


q25=0


q24=0


q23=0


q22=0


q21=0


q20=3*q6


q19= - 8*q3 + 3*q7


q18=0


q17=0


q16= - 2*q3


q15=0


q14= - 2*q6


q13=2*q3 - q7


        2
q12= - ---*q9
        5


q11=0


q10=3*q6


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


q5=0


q4=0


q2=0


q1=0


p7=0


p6=0


p5=0


p3=0


p2= - p4


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, p4

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.

 
{p2,

 p4,

 40*g0011*q3 + 30*g0017*q6 - 80*g0018*q3 + 30*g0018*q7 - 20*g0021*q3

  - 20*g0023*q6 + 20*g0024*q3 - 10*g0024*q7 - 4*g0025*q9 + 30*g0027*q6

  + 10*g0028*q9 - 10*g0029*q3 + 5*g0029*q7 + 10*g0030*q7 + 10*g0031*q6

  + 10*g0034*q3 + 10*g0039*p4 - 10*g0041*p4,

 40*g0052*q3 + 30*g0058*q6 - 80*g0059*q3 + 30*g0059*q7 - 20*g0062*q3

  - 20*g0064*q6 + 20*g0065*q3 - 10*g0065*q7 - 4*g0066*q9 + 30*g0068*q6

  + 10*g0069*q9 - 10*g0070*q3 + 5*g0070*q7 + 10*g0071*q7 + 10*g0072*q6

  + 10*g0075*q3}

Relevance for the application:

The equation:


                        2
f = - Df *Df*f*p4 + (Df) *f *p4
 t      x                  x

The symmetry:

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

        2                    4                  3
 - (Df ) *Df*f *q7 + Df *(Df) *f*q9 - 2*Df *(Df) *f *q6 - 8*Df *f  *f *f*q3
      x       x        x                  x        x          x  2x  x

                        2      5               2
 + 3*Df *f  *f *f*q7 - ---*(Df) *f *q9 + 3*(Df) *f  *f *f*q6 + 4*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))*f(1)*p4 + d(1,f(1))**2*df(f(1),x)*p4$

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