Solution 3 to problem N1t6s8f1
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t6s8f1
Expressions
The solution is given through the following expressions:
q13=0
q12=0
q11=0
q10=0
q9=0
q8=0
q7=0
2
---*p4*q4
3
q6=-----------
p2
q5=0
q3=0
q2=0
q1=0
p7=0
p6=0
p5=0
p3=0
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:
q4, p4, 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.
{2*g0030*p4 + 3*g0032*p2,
q4,
2
2*g0011*p4*q4 + 3*g0013*p2*q4 + 3*g0019*p2*p4 + 3*g0021*p2 ,
p2,
g0039*p4 + g0041*p2}
Relevance for the application:
The equation:
2
f =Df *Df*f*p2 + (Df) *f *p4
t x x
The symmetry:
2 2 3
Df *(Df) *f*p2*q4 + ---*(Df) *f *p4*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)*p4$
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
)*p4*q4)/p2$