Solution 1 to problem N1t6s12f3
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem N1t6s12f3
Expressions
The solution is given through the following expressions:
q12=0
q11= - 2*q6
q10=0
q9=0
q8=0
q7=0
q5=0
q4=0
q3= - q6
q2= - q6
q1=0
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:
q6, 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.
{q3,p1,p2,q6,2*g0005*q6 - g0010*q6 + g0013*q6 + g0014*q6 + g0016*p1 - g0017*p1,
q11}
Relevance for the application:
The equation:
f =Df *f*p1 - Df*f *p1
t x x
The symmetry:
2
f = - Df *Df*f*q6 - (Df ) *f*q6 + Df *Df*f *q6 - 2*f *f *f*q6
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))*f(1)*p1 - d(1,f(1))*df(f(1),x)*p1$
The symmetry:
df(f(1),s)= - d(1,df(f(1),x,2))*d(1,f(1))*f(1)*q6 - d(1,df(f(1),x))**2*f(1)*q6 +
d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q6 - 2*df(f(1),x,2)*df(f(1),x)*f(1)*q6$