Solution 1 to problem N1t10s12f3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t10s12f3

Expressions

The solution is given through the following expressions:


q12=0


q11=3*q2


q10=0


q9=0


q8=0


q7=0


q6= - 2*q2


q5=0


q4=0


q3=q2


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:

 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.

 
{q3,q2,p2,p3,3*g0005*q2 - 2*g0010*q2 + g0013*q2 + g0014*q2 - g0019*p2 + g0020*p2

 }

Relevance for the application:

The equation:


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

The symmetry:

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