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$