Solution 1 to problem N1t2s8f1


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s8f1

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:
 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.
 
{g0018*q13 + g0019*q12 + g0020*q11 + g0021*q10 + g0022*q9 + g0023*q8 + g0024*q7

  + g0025*q6 + g0026*q5 + g0027*q4 + g0028*q3 + g0029*q2 + g0030*q1,

 g0005*q12 + g0006*q11 + g0007*q10 + g0008*q9 + g0009*q8 + g0010*q7 + g0011*q6

  + g0012*q5 + g0013*q4 + g0014*q3 + g0015*q2 + g0016*q1,

 p2}


Relevance for the application:



The equation: 


f =f *p2
 t  x
The symmetry:
                                                2                2
f =Df  *f*q1 + Df  *Df*f*q2 + Df  *f *q8 + (Df ) *f*q3 + Df *(Df) *f*q4
 s   3x          2x             2x  x         x            x

                                   4            3             2
 + Df *Df*f *q7 + Df *f  *q9 + (Df) *f*q5 + (Df) *f *q6 + (Df) *f  *q10
     x     x        x  2x                          x             2x

 + Df*f  *q11 + f  *q13 + f  *f *f*q12
       3x        4x        2x  x
And now in machine readable form:

The system:

df(f(1),t)=df(f(1),x)*p2$
The symmetry:
df(f(1),s)=d(1,df(f(1),x,3))*f(1)*q1 + d(1,df(f(1),x,2))*d(1,f(1))*f(1)*q2 + d(1
,df(f(1),x,2))*df(f(1),x)*q8 + d(1,df(f(1),x))**2*f(1)*q3 + d(1,df(f(1),x))*d(1,
f(1))**2*f(1)*q4 + d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q7 + d(1,df(f(1),x))*df(
f(1),x,2)*q9 + d(1,f(1))**4*f(1)*q5 + d(1,f(1))**3*df(f(1),x)*q6 + d(1,f(1))**2*
df(f(1),x,2)*q10 + d(1,f(1))*df(f(1),x,3)*q11 + df(f(1),x,4)*q13 + df(f(1),x,2)*
df(f(1),x)*f(1)*q12$