Solution 8 to problem N1t10s14f3
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t10s14f3
Expressions
The solution is given through the following expressions:
q16=0
q15=0
q14=0
q13=0
q12=0
q11=0
q10=0
q9=0
q8=0
q7=0
q6=0
q3=0
q2=0
q1=0
p7=0
p6=0
p5=0
p4=0
p1=0
2*p3*q4
q5=---------
3*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:
q4, p2, p3
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.
{2*g0037*p3 + 3*g0038*p2,p2,g0046*p3 + g0047*p2}
Relevance for the application:
The equation:
2
f =Df *Df*f*p2 + (Df) *f *p3
t x x
The symmetry:
2 2 3
Df *(Df) *f*p2*q4 + ---*(Df) *f *p3*q4
x 3 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)*p2 + d(1,f(1))**2*df(f(1),x)*p3$
The symmetry:
df(f(1),s)=(d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p2*q4 + 2/3*d(1,f(1))**3*df(f(1),x
)*p3*q4)/p2$