Solution 1 to problem N1t12s14f4

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t12s14f4

Expressions

The solution is given through the following expressions:


q6=0


q5=3*q1


q4=0


q3= - 2*q1


q2=q1


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:

 q1, 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.

 
{q2,q1,p1,p2,3*g0005*q1 - 2*g0007*q1 + g0008*q1 + g0009*q1 - g0010*p1 + g0011*p1

 }

Relevance for the application:

The equation:


                     2
f =Df *Df*f*p1 - (Df) *f *p1
 t   x                  x

The symmetry:

                       2
f =Df  *Df*f*q1 + (Df ) *f*q1 - 2*Df *Df*f *q1 + 3*f  *f *f*q1
 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)*p1 - d(1,f(1))**2*df(f(1),x)*p1$

The symmetry:

df(f(1),s)=d(1,df(f(1),x,2))*d(1,f(1))*f(1)*q1 + d(1,df(f(1),x))**2*f(1)*q1 - 2*
d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q1 + 3*df(f(1),x,2)*df(f(1),x)*f(1)*q1$