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$