Solution 1 to problem N2t2s8f3

Expressions | Parameters | Inequalities | Relevance | Back to problem N2t2s8f3

Expressions

The solution is given through the following expressions:


q13=q6


q12=q7


q11= - q7


q10=q6


q9=q6


q8= - q7


q5=0


q4=0


q3=0


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:

 q15, q14, q7, q6, 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*q14 + g0004*q6 + g0005*q7 + g0006*q6 + g0007*q6 + g0008*q7 + g0009*q6

  + g0013*p1,

 p1,

 g0038*p2 + g0039*p1,

 g0014*q14 + g0015*q6 + g0016*q7 - g0017*q7 - g0018*q7 + g0019*q7 + g0020*q6

  + g0024*p1,

 g0025*q6 + g0026*q7 - g0027*q7 + g0028*q6 + g0029*q6 - g0030*q7 + g0031*q7

  + g0032*q6}

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*q7 + D f *f *q6 + D f*D D f *q7 + D f*f  *q6 + D D f  *q14
 s  2 x  1 2        2 x  x       2   1 2 x       2   2x       1 2 3x

 + D D f *D f*q6 + D D f*D f *q6 - D f *f *q7 - D f*f  *q7 + f  *q15
    1 2 x  1        1 2   1 x       1 x  x       1   2x       4x

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,df(f(1),x))*d(1,d(2,f(1)))*q7 + d(2,df(f(1),x))*df(f(1),x)*q6 + d
(2,f(1))*d(1,d(2,df(f(1),x)))*q7 + d(2,f(1))*df(f(1),x,2)*q6 + d(1,d(2,df(f(1),x
,3)))*q14 + d(1,d(2,df(f(1),x)))*d(1,f(1))*q6 + d(1,d(2,f(1)))*d(1,df(f(1),x))*
q6 - d(1,df(f(1),x))*df(f(1),x)*q7 - d(1,f(1))*df(f(1),x,2)*q7 + df(f(1),x,4)*
q15$