Solution 1 to problem N1t11s12f2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t11s12f2

Expressions

The solution is given through the following expressions:


q9=0


       10
q8= - ----*q5
       3


q7=0


q6=0


q4=2*q5


       2
q3= - ---*q5
       3


       4
q2= - ---*q5
       3


q1=0


p7=0


p6=0


p5=0


p4=0


p3= - p2


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:

 q5, 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.

 
{q4,q5,p2,p3}

Relevance for the application:

The equation:


           2            3
f =Df *(Df) *f*p2 - (Df) *f *p2
 t   x                     x

The symmetry:

       2                  4                                         2
f = - ---*Df  *Df*f*q5 - ---*Df  *Df *f*q5 + 2*Df  *Df*f *q5 + (Df ) *f *q5
 s     3    3x            3    2x   x            2x     x         x    x

    10
 - ----*f  *f *f*q5
    3    3x  x

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p2 - d(1,f(1))**3*df(f(1),x)*p2$

The symmetry:

df(f(1),s)= - 2/3*d(1,df(f(1),x,3))*d(1,f(1))*f(1)*q5 - 4/3*d(1,df(f(1),x,2))*d(
1,df(f(1),x))*f(1)*q5 + 2*d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*q5 + d(1,df(f(1
),x))**2*df(f(1),x)*q5 - 10/3*df(f(1),x,3)*df(f(1),x)*f(1)*q5$