Solution 8 to problem N1f1b0o35w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o35w1

Expressions

The solution is given through the following expressions: 

q21=0


q20=4*q2


q19=0


q18=0


q17=0


q16=0


q15=0


q14=0


q13=3*q3


q12=0


q11= - 2*q2


q10= - q2


q9= - 2*q3


       1
q8= - ---*q5
       2


q7=0


q6=2*q3


q4=2*q2


q1=0


p7=0


p6=0


p5=0


p3=0


p2= - p4


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: 
 q5, q3, q2, p4

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. 
 
{8*g0030*q2 + 6*g0037*q3 - 4*g0039*q2 - 2*g0040*q2 - 4*g0041*q3 - g0042*q5

  + 4*g0044*q3 + 2*g0045*q5 + 4*g0046*q2 + 2*g0047*q3 + 2*g0048*q2,

 8*g0003*q2 + 6*g0010*q3 - 4*g0012*q2 - 2*g0013*q2 - 4*g0014*q3 - g0015*q5

  + 4*g0017*q3 + 2*g0018*q5 + 4*g0019*q2 + 2*g0020*q3 + 2*g0021*q2 + 2*g0025*p4

  - 2*g0027*p4,

 p2,

 p4}

Relevance for the application:



The equation: 



                        2
f = - Df *Df*f*p4 + (Df) *f *p4
 t      x                  x


The symmetry: 

                                             2
f =Df  *Df*f*q2 + 2*Df  *Df *f*q2 + Df  *(Df) *f*q3 - 2*Df  *Df*f *q2
 s   3x               2x   x          2x                  2x     x

          2                2                 3                  2
 + 2*(Df ) *Df*f*q3 - (Df ) *f *q2 + Df *(Df) *f*q5 - 2*Df *(Df) *f *q3
        x                x    x        x                  x        x

    1      4
 - ---*(Df) *f *q5 + 3*Df*f  *f *f*q3 + 4*f  *f *f*q2
    2         x            2x  x           3x  x


And now in machine readable form: 

The system: 

df(f(1),t)= - d(1,df(f(1),x))*d(1,f(1))*f(1)*p4 + d(1,f(1))**2*df(f(1),x)*p4$


The symmetry: 

df(f(1),s)=d(1,df(f(1),x,3))*d(1,f(1))*f(1)*q2 + 2*d(1,df(f(1),x,2))*d(1,df(f(1)
,x))*f(1)*q2 + d(1,df(f(1),x,2))*d(1,f(1))**2*f(1)*q3 - 2*d(1,df(f(1),x,2))*d(1,
f(1))*df(f(1),x)*q2 + 2*d(1,df(f(1),x))**2*d(1,f(1))*f(1)*q3 - d(1,df(f(1),x))**
2*df(f(1),x)*q2 + d(1,df(f(1),x))*d(1,f(1))**3*f(1)*q5 - 2*d(1,df(f(1),x))*d(1,f
(1))**2*df(f(1),x)*q3 - 1/2*d(1,f(1))**4*df(f(1),x)*q5 + 3*d(1,f(1))*df(f(1),x,2
)*df(f(1),x)*f(1)*q3 + 4*df(f(1),x,3)*df(f(1),x)*f(1)*q2$