Solution 1 to problem N1t8s12f2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s12f2

Expressions

The solution is given through the following expressions:


q9=0


q8=2*q2


q7=0


q6=0


       1
q5= - ---*q2
       2


q4= - q2


    1
q3=---*q2
    2


q1=0


p3=0


p1= - p2

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:

 q2, p2

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.

 
{p1,

 p2,

 q2,

 4*g0005*q2 - g0008*q2 - 2*g0009*q2 + g0010*q2 + 2*g0011*q2 + 2*g0013*p2

  - 2*g0014*p2,

 q3}

Relevance for the application:

The equation:


                        2
f = - Df *Df*f*p2 + (Df) *f *p2
 t      x                  x

The symmetry:

    1                                                  1       2
f =---*Df  *Df*f*q2 + Df  *Df *f*q2 - Df  *Df*f *q2 - ---*(Df ) *f *q2
 s  2    3x             2x   x          2x     x       2     x    x

 + 2*f  *f *f*q2
      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)*p2 + d(1,f(1))**2*df(f(1),x)*p2$

The symmetry:

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