Solution 2 to problem N2t2s6f3

Expressions | Parameters | Inequalities | Relevance | Back to problem N2t2s6f3

Expressions

The solution is given through the following expressions:


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:

 q8, q7, q6, q5, q4, q3, q2, q1, 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.

 
{g0015*q6 + g0016*q5 + g0017*q4 + g0018*q3 + g0019*q2 + g0020*q1,

 g0003*q7 + g0004*q5 + g0005*q4 + g0006*q3 + g0007*q1,

 g0009*q7 + g0010*q6 + g0011*q4 + g0012*q3 + g0013*q2,

 p2}

Relevance for the application:

The equation:


f =f *p2
 t  x

The symmetry:

f =D f *f*q1 + D f*D D f*q3 + D f*f *q5 + D D f  *q7 + D D f*D f*q4 + D f *f*q2
 s  2 x         2   1 2        2   x       1 2 2x       1 2   1        1 x

 + D f*f *q6 + f  *q8
    1   x       3x

And now in machine readable form:

The system:

df(f(1),t)=df(f(1),x)*p2$

The symmetry:

df(f(1),s)=d(2,df(f(1),x))*f(1)*q1 + d(2,f(1))*d(1,d(2,f(1)))*q3 + d(2,f(1))*df(
f(1),x)*q5 + d(1,d(2,df(f(1),x,2)))*q7 + d(1,d(2,f(1)))*d(1,f(1))*q4 + d(1,df(f(
1),x))*f(1)*q2 + d(1,f(1))*df(f(1),x)*q6 + df(f(1),x,3)*q8$