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$