Solution 5 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


        2        1
q27= - ---*q3 + ---*q7
        3        6


               3
q26= - 3*q3 + ---*q7
               2


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


          1
q19=q3 + ---*q7
          2


q18=0


q17=0


          1
q16=q3 - ---*q7
          2


q15=0


q14=0


q13= - q3


q12=0


q11=0


q10=0


q9=0


q8=q3


q6=0


q5=0


q4=0


q2=0


q1=0


p13=0


p12=2*p3


p11=0


p10=0


p9=0


p8=0


p7= - p3


p6=0


p5=0


p4=0


p2=p3


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:

 q7, 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.

 
{4*g0059*q3 - g0059*q7 + 18*g0060*q3 - 9*g0060*q7 - 6*g0067*q3 - 3*g0067*q7

  - 6*g0070*q3 + 3*g0070*q7 + 6*g0073*q3 - 6*g0078*q3 - 6*g0079*q7 - 6*g0083*q3,

 4*g0012*q3 - g0012*q7 + 18*g0013*q3 - 9*g0013*q7 - 6*g0020*q3 - 3*g0020*q7

  - 6*g0023*q3 + 3*g0023*q7 + 6*g0026*q3 - 6*g0031*q3 - 6*g0032*q7 - 6*g0036*q3

  - 12*g0039*p3 + 6*g0044*p3 - 6*g0048*p3 - 6*g0049*p3,

 p3,

 p2}

Relevance for the application:

The equation:


                       2
f =Df  *Df*f*p3 + (Df ) *f*p3 - Df *Df*f *p3 + 2*f  *f *f*p3
 t   2x              x            x     x         2x  x

The symmetry:

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

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

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

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x,2))*d(1,f(1))*f(1)*p3 + d(1,df(f(1),x))**2*f(1)*p3 - d(
1,df(f(1),x))*d(1,f(1))*df(f(1),x)*p3 + 2*df(f(1),x,2)*df(f(1),x)*f(1)*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))**2*df(f(1),x)*q3 - 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))**3*f(1)*q3 - d(1,df(
f(1),x))**2*d(1,f(1))*df(f(1),x)*q3 + 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 - 2/3*d(1,f(1))**3*
df(f(1),x,3)*q3 + 1/6*d(1,f(1))**3*df(f(1),x,3)*q7 - 3*d(1,f(1))*df(f(1),x,3)*df
(f(1),x)*f(1)*q3 + 3/2*d(1,f(1))*df(f(1),x,3)*df(f(1),x)*f(1)*q7$