Solution 1 to problem N1t12s14f4
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t12s14f4
Expressions
The solution is given through the following expressions:
q6=0
q5=3*q1
q4=0
q3= - 2*q1
q2=q1
p3=0
p2= - p1
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:
q1, 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.
{q2,q1,p1,p2,3*g0005*q1 - 2*g0007*q1 + g0008*q1 + g0009*q1 - g0010*p1 + g0011*p1
}
Relevance for the application:
The equation:
2
f =Df *Df*f*p1 - (Df) *f *p1
t x x
The symmetry:
2
f =Df *Df*f*q1 + (Df ) *f*q1 - 2*Df *Df*f *q1 + 3*f *f *f*q1
s 2x x x x 2x x
And now in machine readable form:
The system:
df(f(1),t)=d(1,df(f(1),x))*d(1,f(1))*f(1)*p1 - d(1,f(1))**2*df(f(1),x)*p1$
The symmetry:
df(f(1),s)=d(1,df(f(1),x,2))*d(1,f(1))*f(1)*q1 + d(1,df(f(1),x))**2*f(1)*q1 - 2*
d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q1 + 3*df(f(1),x,2)*df(f(1),x)*f(1)*q1$