Solution 1 to problem N2t2s6f3

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

Expressions

The solution is given through the following expressions:


q6= - q3


q5=q4


q2=0


q1=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, q4, q3, p2, 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.

 
{g0003*q7 + g0004*q4 + g0005*q4 + g0006*q3 + g0008*p1,

 g0021*p2 + g0022*p1,

 p1,

 g0009*q7 - g0010*q3 + g0011*q4 + g0012*q3 + g0014*p1,

 g0015*q3 - g0016*q4 - g0017*q4 - g0018*q3}

Relevance for the application:

The equation:


f =D D f*p1 + f *p2
 t  1 2        x

The symmetry:

f =D f*D D f*q3 + D f*f *q4 + D D f  *q7 + D D f*D f*q4 - D f*f *q3 + f  *q8
 s  2   1 2        2   x       1 2 2x       1 2   1        1   x       3x

And now in machine readable form:

The system:

df(f(1),t)=d(1,d(2,f(1)))*p1 + df(f(1),x)*p2$

The symmetry:

df(f(1),s)=d(2,f(1))*d(1,d(2,f(1)))*q3 + d(2,f(1))*df(f(1),x)*q4 + d(1,d(2,df(f(
1),x,2)))*q7 + d(1,d(2,f(1)))*d(1,f(1))*q4 - d(1,f(1))*df(f(1),x)*q3 + df(f(1),x
,3)*q8$