Solution 1 to problem N1t11s13f2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t11s13f2

Expressions

The solution is given through the following expressions:


q11=0


q10=0


q9=0


q8=0


q7=0


q6=4*q2


q5= - 3*q2


q4=0


q3=2*q2


q1=0


p7=0


p6=0


p5=0


p4=0


p2= - p3


p1=0

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, p3

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.

 
{p2,q2,p3}

Relevance for the application:

The equation:


              2            3
f = - Df *(Df) *f*p3 + (Df) *f *p3
 t      x                     x

The symmetry:

            2               2                     2
f =Df  *(Df) *f*q2 + 2*(Df ) *Df*f*q2 - 3*Df *(Df) *f *q2 + 4*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))**2*f(1)*p3 + d(1,f(1))**3*df(f(1),x)*p3$

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 - 3*d(1,df(f(1),x))*d(1,f(1))**2*df(f(1),x)*q2 + 4*d(1,f(1))*df(f(1),
x,2)*df(f(1),x)*f(1)*q2$