Solution 1 to problem N1t8s13f2
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t8s13f2
Expressions
The solution is given through the following expressions:
q11=0
q10=0
q9=0
q8=0
q7=0
q6=3*q2
q5= - 2*q2
q4=0
q3=2*q2
q1=0
p3=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:
q2, 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.
{p1,q2,p2}
Relevance for the application:
The equation:
2
f = - Df *Df*f*p2 + (Df) *f *p2
t x x
The symmetry:
2 2 2
f =Df *(Df) *f*q2 + 2*(Df ) *Df*f*q2 - 2*Df *(Df) *f *q2 + 3*Df*f *f *f*q2
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)*p2 + d(1,f(1))**2*df(f(1),x)*p2$
The symmetry:
df(f(1),s)=d(1,df(f(1),x,2))*d(1,f(1))**2*f(1)*q2 + 2*d(1,df(f(1),x))**2*d(1,f(1
))*f(1)*q2 - 2*d(1,df(f(1),x))*d(1,f(1))**2*df(f(1),x)*q2 + 3*d(1,f(1))*df(f(1),
x,2)*df(f(1),x)*f(1)*q2$