Solution 1 to problem N1t11s14f2
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t11s14f2
Expressions
The solution is given through the following expressions:
q14=0
q13=0
q12=0
q11=0
q10=0
q9=0
q8=0
q7=0
q6=0
q4=0
q3=0
q2=0
p7=0
p6=0
p5=0
p4=0
p1=0
4*p2*q5
q1=---------
3*p3
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, p3, 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.
{3*g0014*p3 + 4*g0018*p2,g0023*p3 + g0024*p2,p3}
Relevance for the application:
The equation:
2 3
f =Df *(Df) *f*p2 + (Df) *f *p3
t x x
The symmetry:
4 3 4
---*Df *(Df) *f*p2*q5 + (Df) *f *p3*q5
3 x x
f =----------------------------------------
s p3
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)*p3$
The symmetry:
df(f(1),s)=(4/3*d(1,df(f(1),x))*d(1,f(1))**3*f(1)*p2*q5 + d(1,f(1))**4*df(f(1),x
)*p3*q5)/p3$