Solution 3 to problem N1t6s10f3
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t6s10f3
Expressions
The solution is given through the following expressions:
q7=0
q6=0
q5=0
q4=0
1
---*p2*q2
2
q3=-----------
p1
q1=0
p3=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, 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.
{g0021*p2 + g0022*p1,
p1,
2
g0008*p2*q2 + 2*g0009*p1*q2 + 2*g0011*p1*p2 + 2*g0012*p1 ,
q2,
g0017*p2 + 2*g0018*p1}
Relevance for the application:
The equation:
f =Df *f*p1 + Df*f *p2
t x x
The symmetry:
1 2
Df *Df*f*p1*q2 + ---*(Df) *f *p2*q2
x 2 x
f =-------------------------------------
s p1
And now in machine readable form:
The system:
df(f(1),t)=d(1,df(f(1),x))*f(1)*p1 + d(1,f(1))*df(f(1),x)*p2$
The symmetry:
df(f(1),s)=(d(1,df(f(1),x))*d(1,f(1))*f(1)*p1*q2 + 1/2*d(1,f(1))**2*df(f(1),x)*
p2*q2)/p1$