Solution 1 to problem N1t2s8b1


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s8b1

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:
 q11, q10, q9, 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.
 
{g0005*q3 + g0006*q2 + g0007*q1,p2}


Relevance for the application:



The equation: 


b =b *p2
 t  x
The symmetry:
    9                              3                                    2
b =b *q10 + Db  *Db*b*q3 + Db *Db*b *q2 + Db *Db*b *q1 + b  *q11 + b  *b *q4
 s            2x             x              x     x       4x        3x

        4                      3        2  3          6
 + b  *b *q6 + b  *b *b*q5 + b  *q9 + b  *b *q7 + b *b *q8
    2x          2x  x         x        x           x
And now in machine readable form:

The system:

df(b(1),t)=df(b(1),x)*p2$
The symmetry:
df(b(1),s)=b(1)**9*q10 + d(1,df(b(1),x,2))*d(1,b(1))*b(1)*q3 + d(1,df(b(1),x))*d
(1,b(1))*b(1)**3*q2 + d(1,df(b(1),x))*d(1,b(1))*df(b(1),x)*q1 + df(b(1),x,4)*q11
 + df(b(1),x,3)*b(1)**2*q4 + df(b(1),x,2)*b(1)**4*q6 + df(b(1),x,2)*df(b(1),x)*b
(1)*q5 + df(b(1),x)**3*q9 + df(b(1),x)**2*b(1)**3*q7 + df(b(1),x)*b(1)**6*q8$