Solution 1 to problem N1t5s12f2
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t5s12f2
Expressions
The solution is given through the following expressions:
q9=0
q8= - 6*q5
q7=0
q6=0
q4=2*q5
q3= - 2*q5
q2= - 4*q5
q1=0
p1= - 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:
q5, 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.
{q3,q5,p2,p1}
Relevance for the application:
The equation:
f = - Df *f*p2 + Df*f *p2
t x x
The symmetry:
2
f = - 2*Df *Df*f*q5 - 4*Df *Df *f*q5 + 2*Df *Df*f *q5 + (Df ) *f *q5
s 3x 2x x 2x x x x
- 6*f *f *f*q5
3x x
And now in machine readable form:
The system:
df(f(1),t)= - d(1,df(f(1),x))*f(1)*p2 + d(1,f(1))*df(f(1),x)*p2$
The symmetry:
df(f(1),s)= - 2*d(1,df(f(1),x,3))*d(1,f(1))*f(1)*q5 - 4*d(1,df(f(1),x,2))*d(1,df
(f(1),x))*f(1)*q5 + 2*d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*q5 + d(1,df(f(1),x)
)**2*df(f(1),x)*q5 - 6*df(f(1),x,3)*df(f(1),x)*f(1)*q5$