Solution 2 to problem N2t2s8f3

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

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: 
 q15, q14, q13, q12, 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. 
 
{g0025*q13 + g0026*q12 + g0027*q11 + g0028*q10 + g0029*q9 + g0030*q8 + g0031*q7

  + g0032*q6 + g0033*q5 + g0034*q4 + g0035*q3 + g0036*q2 + g0037*q1,

 g0003*q14 + g0004*q13 + g0005*q12 + g0006*q10 + g0007*q9 + g0008*q7 + g0009*q6

  + g0010*q5 + g0011*q2 + g0012*q1,

 g0014*q14 + g0015*q13 + g0016*q12 + g0017*q11 + g0018*q8 + g0019*q7 + g0020*q6

  + g0021*q4 + g0022*q3 + g0023*q2,

 p2}

Relevance for the application:



The equation: 



f =f *p2
 t  x


The symmetry: 

                                                  2
f =D f  *f*q5 + D f *D D f*q7 + D f *f *q9 + (D f) *f*q1 + D f*D D f *q12
 s  2 2x         2 x  1 2        2 x  x        2            2   1 2 x

 + D f*D f*f*q2 + D f*f  *q10 + D D f  *q14 + D D f *D f*q13 + D D f*D f *q6
    2   1          2   2x        1 2 3x        1 2 x  1         1 2   1 x

                                  2
 + D f  *f*q4 + D f *f *q8 + (D f) *f*q3 + D f*f  *q11 + f  *q15
    1 2x         1 x  x        1            1   2x        4x


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,2))*f(1)*q5 + d(2,df(f(1),x))*d(1,d(2,f(1)))*q7 + d(2,
df(f(1),x))*df(f(1),x)*q9 + d(2,f(1))**2*f(1)*q1 + d(2,f(1))*d(1,d(2,df(f(1),x))
)*q12 + d(2,f(1))*d(1,f(1))*f(1)*q2 + d(2,f(1))*df(f(1),x,2)*q10 + d(1,d(2,df(f(
1),x,3)))*q14 + d(1,d(2,df(f(1),x)))*d(1,f(1))*q13 + d(1,d(2,f(1)))*d(1,df(f(1),
x))*q6 + d(1,df(f(1),x,2))*f(1)*q4 + d(1,df(f(1),x))*df(f(1),x)*q8 + d(1,f(1))**
2*f(1)*q3 + d(1,f(1))*df(f(1),x,2)*q11 + df(f(1),x,4)*q15$