Solution 7 to problem N1t10s14f3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t10s14f3

Expressions

The solution is given through the following expressions:


q16=0


q15= - 2*q7


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


    1
q6=---*q7
    2


       3
q4= - ---*q5
       2


q3= - q7


       1
q2= - ---*q7
       2


q1=0


p7=0


p6=0


p5=0


p4=0


p3= - p2


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, q7, 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.

 
{q3,

 q7,

 p3,

 p2,

 q2,

 4*g0005*q7 - 2*g0013*q7 - g0014*q7 - 2*g0015*q5 + 3*g0016*q5 + 2*g0017*q7

  + g0018*q7 + 2*g0023*p2 - 2*g0024*p2,

 q6,

 4*g0027*q7 - 2*g0035*q7 - g0036*q7 - 2*g0037*q5 + 3*g0038*q5 + 2*g0039*q7

  + g0040*q7}

Relevance for the application:

The equation:


                     2
f =Df *Df*f*p2 - (Df) *f *p2
 t   x                  x

The symmetry:

       1                                                  1       2
f = - ---*Df  *Df*f*q7 - Df  *Df *f*q7 + Df  *Df*f *q7 + ---*(Df ) *f *q7
 s     2    3x             2x   x          2x     x       2     x    x

    3          2            3
 - ---*Df *(Df) *f*q5 + (Df) *f *q5 - 2*f  *f *f*q7
    2    x                     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)*p2 - d(1,f(1))**2*df(f(1),x)*p2$

The symmetry:

df(f(1),s)= - 1/2*d(1,df(f(1),x,3))*d(1,f(1))*f(1)*q7 - d(1,df(f(1),x,2))*d(1,df
(f(1),x))*f(1)*q7 + d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*q7 + 1/2*d(1,df(f(1),
x))**2*df(f(1),x)*q7 - 3/2*d(1,df(f(1),x))*d(1,f(1))**2*f(1)*q5 + d(1,f(1))**3*
df(f(1),x)*q5 - 2*df(f(1),x,3)*df(f(1),x)*f(1)*q7$