Solution 2 to problem N1t4s10f1


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t4s10f1

Expressions

The solution is given through the following expressions:

q21=0


q20= - 6*q10


q19=0


q18=0


q17=0


q16=0


q15=0


q14=0


q12=0


q11=2*q10


q7=0


q6= - 2*q9


q5= - 4*q8


q4= - 4*q10


q3= - q9


q2= - 2*q10


q1=0


p4=0


p3= - p1


p2=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:
 q13, q9, q8, q10, p1

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.
 
{6*g0029*q10 + 2*g0036*q9 - 2*g0038*q10 - g0039*q10 - g0040*q9 - g0041*q8

  + 2*g0043*q9 + 4*g0044*q8 + 4*g0045*q10 + g0046*q9 + 2*g0047*q10,

 6*g0005*q10 + 2*g0012*q9 - 2*g0014*q10 - g0015*q10 - g0016*q9 - g0017*q8

  + 2*g0019*q9 + 4*g0020*q8 + 4*g0021*q10 + g0022*q9 + 2*g0023*q10 + g0025*p1

  - g0027*p1,

 p3,

 p1}


Relevance for the application:



The equation: 


f =Df *f*p1 - Df*f *p1
 t   x            x
The symmetry:
                                                    2
f = - 2*Df  *Df*f*q10 - 4*Df  *Df *f*q10 - Df  *(Df) *f*q9 + 2*Df  *Df*f *q10
 s        3x                2x   x           2x                  2x     x

          2                2                    3                2
 - 2*(Df ) *Df*f*q9 + (Df ) *f *q10 - 4*Df *(Df) *f*q8 + Df *(Df) *f *q9
        x                x    x           x                x        x

       4
 + (Df) *f *q8 + Df*f  *f *f*q13 - 6*f  *f *f*q10
          x          2x  x            3x  x
And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))*f(1)*p1 - d(1,f(1))*df(f(1),x)*p1$
The symmetry:
df(f(1),s)= - 2*d(1,df(f(1),x,3))*d(1,f(1))*f(1)*q10 - 4*d(1,df(f(1),x,2))*d(1,
df(f(1),x))*f(1)*q10 - d(1,df(f(1),x,2))*d(1,f(1))**2*f(1)*q9 + 2*d(1,df(f(1),x,
2))*d(1,f(1))*df(f(1),x)*q10 - 2*d(1,df(f(1),x))**2*d(1,f(1))*f(1)*q9 + d(1,df(f
(1),x))**2*df(f(1),x)*q10 - 4*d(1,df(f(1),x))*d(1,f(1))**3*f(1)*q8 + d(1,df(f(1)
,x))*d(1,f(1))**2*df(f(1),x)*q9 + d(1,f(1))**4*df(f(1),x)*q8 + d(1,f(1))*df(f(1)
,x,2)*df(f(1),x)*f(1)*q13 - 6*df(f(1),x,3)*df(f(1),x)*f(1)*q10$