Solution 3 to problem N1f1b0o37w3


Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o37w3

Expressions

The solution is given through the following expressions:

q16=0


q15=3*q2


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7= - q2


       1
q6= - ---*q2
       2


       1
q5= - ---*q4
       3


q3=2*q2


q1=0


p3=0


p2= - p1


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:
 q4, q2, 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.
 
{q2,

 p1,

 p2,

 18*g0005*q2 - 6*g0013*q2 - 3*g0014*q2 - 2*g0015*q4 + 6*g0016*q4 + 12*g0017*q2

  + 6*g0018*q2 - 6*g0020*p1 + 6*g0021*p1,

 18*g0023*q2 - 6*g0031*q2 - 3*g0032*q2 - 2*g0033*q4 + 6*g0034*q4 + 12*g0035*q2

  + 6*g0036*q2}


Relevance for the application:



The equation: 


f =Df *f*p1 - Df*f *p1
 t   x            x
The symmetry:
                                                     1       2
f =Df  *Df*f*q2 + 2*Df  *Df *f*q2 - Df  *Df*f *q2 - ---*(Df ) *f *q2
 s   3x               2x   x          2x     x       2     x    x

           2         1      3
 + Df *(Df) *f*q4 - ---*(Df) *f *q4 + 3*f  *f *f*q2
     x               3         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)=d(1,df(f(1),x,3))*d(1,f(1))*f(1)*q2 + 2*d(1,df(f(1),x,2))*d(1,df(f(1)
,x))*f(1)*q2 - d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*q2 - 1/2*d(1,df(f(1),x))**
2*df(f(1),x)*q2 + d(1,df(f(1),x))*d(1,f(1))**2*f(1)*q4 - 1/3*d(1,f(1))**3*df(f(1
),x)*q4 + 3*df(f(1),x,3)*df(f(1),x)*f(1)*q2$