Solution 1 to problem N1t10s11f2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t10s11f2

Expressions

The solution is given through the following expressions:


q7=0


q6=0


q5=0


q4=0


q2= - q3


q1=0


p6=0


p5=4*p2


p4=0


p3= - 3*p2


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:

 q3, 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.

 
{p3,p2,q3,p1}

Relevance for the application:

The equation:


                       2
f =Df  *Df*f*p2 + (Df ) *f*p2 - 3*Df *Df*f *p2 + 4*f  *f *f*p2
 t   2x              x              x     x         2x  x

The symmetry:

              2            3
f = - Df *(Df) *f*q3 + (Df) *f *q3
 s      x                     x

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x,2))*d(1,f(1))*f(1)*p2 + d(1,df(f(1),x))**2*f(1)*p2 - 3*
d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*p2 + 4*df(f(1),x,2)*df(f(1),x)*f(1)*p2$

The symmetry:

df(f(1),s)= - d(1,df(f(1),x))*d(1,f(1))**2*f(1)*q3 + d(1,f(1))**3*df(f(1),x)*q3$