Solution 1 to problem N1t8s11f2
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t8s11f2
Expressions
The solution is given through the following expressions:
q7=0
q6=0
q5=0
q4=0
q1=0
p3=0
3*p1*q3
q2=---------
2*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:
q3, p2, 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.
{g0013*p2 + g0014*p1,2*g0009*p2 + 3*g0010*p1}
Relevance for the application:
The equation:
2
f =Df *Df*f*p1 + (Df) *f *p2
t x x
The symmetry:
3 2 3
---*Df *(Df) *f*p1*q3 + (Df) *f *p2*q3
2 x x
f =----------------------------------------
s p2
And now in machine readable form:
The system:
df(f(1),t)=d(1,df(f(1),x))*d(1,f(1))*f(1)*p1 + d(1,f(1))**2*df(f(1),x)*p2$
The symmetry:
df(f(1),s)=(3/2*d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p1*q3 + d(1,f(1))**3*df(f(1),x
)*p2*q3)/p2$