Solution 2 to problem N2t2s12f3

Expressions | Parameters | Inequalities | Relevance | Back to problem N2t2s12f3

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:

 q49, q48, q47, q46, q45, q44, q43, q42, q41, q40, q39, 
q38, q37, q36, q35, q34, q33, q32, q31, q30, q29, q28, 
q27, q26, q25, q24, q23, q22, q21, q20, q19, q18, q17, 
q16, 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.

 
{g0079*q47 + g0080*q46 + g0081*q45 + g0082*q44 + g0083*q43 + g0084*q42

  + g0085*q41 + g0086*q40 + g0087*q39 + g0088*q38 + g0089*q37 + g0090*q36

  + g0091*q35 + g0092*q34 + g0093*q33 + g0094*q32 + g0095*q31 + g0096*q30

  + g0097*q29 + g0098*q28 + g0099*q27 + g0100*q26 + g0101*q25 + g0102*q24

  + g0103*q23 + g0104*q22 + g0105*q21 + g0106*q20 + g0107*q19 + g0108*q18

  + g0109*q17 + g0110*q16 + g0111*q15 + g0112*q14 + g0113*q13 + g0114*q12

  + g0115*q11 + g0116*q10 + g0117*q9 + g0118*q8 + g0119*q7 + g0120*q6 + g0121*q5

  + g0122*q4 + g0123*q3 + g0124*q2 + g0125*q1,

 g0003*q48 + g0004*q47 + g0005*q46 + g0006*q45 + g0007*q43 + g0008*q42

  + g0009*q40 + g0010*q39 + g0011*q38 + g0012*q37 + g0013*q34 + g0014*q32

  + g0015*q31 + g0016*q30 + g0017*q29 + g0018*q28 + g0019*q27 + g0020*q26

  + g0021*q25 + g0022*q24 + g0023*q22 + g0024*q20 + g0025*q19 + g0026*q18

  + g0027*q17 + g0028*q16 + g0029*q15 + g0030*q14 + g0031*q13 + g0032*q11

  + g0033*q9 + g0034*q8 + g0035*q6 + g0036*q5 + g0037*q3 + g0038*q2 + g0039*q1,

 g0041*q48 + g0042*q47 + g0043*q46 + g0044*q45 + g0045*q43 + g0046*q42

  + g0047*q41 + g0048*q39 + g0049*q38 + g0050*q36 + g0051*q35 + g0052*q33

  + g0053*q32 + g0054*q30 + g0055*q29 + g0056*q28 + g0057*q27 + g0058*q26

  + g0059*q25 + g0060*q23 + g0061*q22 + g0062*q21 + g0063*q19 + g0064*q18

  + g0065*q17 + g0066*q16 + g0067*q15 + g0068*q14 + g0069*q12 + g0070*q11

  + g0071*q10 + g0072*q8 + g0073*q7 + g0074*q6 + g0075*q4 + g0076*q3 + g0077*q2,

 p2}

Relevance for the application:

The equation:


f =f *p2
 t  x

The symmetry:

f =D f  *f*q13 + D f  *D D f*q14 + D f  *f *q20 + D f  *D f*f*q9
 s  2 4x          2 3x  1 2         2 3x  x        2 2x  2

                                                             2
 + D f  *D D f *q29 + D f  *D f*f*q8 + D f  *f  *q34 + (D f ) *f*q5
    2 2x  1 2 x        2 2x  1          2 2x  2x         2 x

 + D f *D f*D D f*q18 + D f *D f*f *q24 + D f *D D f  *q39 + D f *D D f*D f*q19
    2 x  2   1 2         2 x  2   x        2 x  1 2 2x        2 x  1 2   1

                                                          3
 + D f *D f *f*q6 + D f *D f*f *q25 + D f *f  *q37 + (D f) *f*q1
    2 x  1 x         2 x  1   x        2 x  3x         2

        2                   2                 2
 + (D f) *D D f *q26 + (D f) *D f*f*q3 + (D f) *f  *q31 + D f*D D f  *q42
     2     1 2 x         2     1           2     2x        2   1 2 3x

 + D f*D D f *D f*q27 + D f*D D f*D f *q16 + D f*D f  *f*q11 + D f*D f *f *q22
    2   1 2 x  1         2   1 2   1 x        2   1 2x          2   1 x  x

            2
 + D f*(D f) *f*q2 + D f*D f*f  *q32 + D f*f  *q40 + D D f  *q48
    2    1            2   1   2x        2   4x        1 2 5x

 + D D f  *D f*q43 + D D f  *D f *q38 + D D f *D D f*f*q47 + D D f *D f  *q30
    1 2 3x  1         1 2 2x  1 x        1 2 x  1 2           1 2 x  1 2x

               2
 + D D f *(D f) *q28 + D D f *f *f*q46 + D D f*D f  *q15 + D D f*D f *D f*q17
    1 2 x   1           1 2 x  x          1 2   1 3x        1 2   1 x  1

 - D D f*f  *f*q45 + D f  *f*q12 + D f  *f *q21 + D f  *D f*f*q10
    1 2   2x          1 4x          1 3x  x        1 2x  1

                         2                                              3
 + D f  *f  *q35 + (D f ) *f*q7 + D f *D f*f *q23 + D f *f  *q36 + (D f) *f*q4
    1 2x  2x         1 x           1 x  1   x        1 x  3x         1

        2
 + (D f) *f  *q33 + D f*f  *q41 + f  *q49 + f  *f *f*q44
     1     2x        1   4x        6x        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(2,df(f(1),x,4))*f(1)*q13 + d(2,df(f(1),x,3))*d(1,d(2,f(1)))*q14 + d
(2,df(f(1),x,3))*df(f(1),x)*q20 + d(2,df(f(1),x,2))*d(2,f(1))*f(1)*q9 + d(2,df(f
(1),x,2))*d(1,d(2,df(f(1),x)))*q29 + d(2,df(f(1),x,2))*d(1,f(1))*f(1)*q8 + d(2,
df(f(1),x,2))*df(f(1),x,2)*q34 + d(2,df(f(1),x))**2*f(1)*q5 + d(2,df(f(1),x))*d(
2,f(1))*d(1,d(2,f(1)))*q18 + d(2,df(f(1),x))*d(2,f(1))*df(f(1),x)*q24 + d(2,df(f
(1),x))*d(1,d(2,df(f(1),x,2)))*q39 + d(2,df(f(1),x))*d(1,d(2,f(1)))*d(1,f(1))*
q19 + d(2,df(f(1),x))*d(1,df(f(1),x))*f(1)*q6 + d(2,df(f(1),x))*d(1,f(1))*df(f(1
),x)*q25 + d(2,df(f(1),x))*df(f(1),x,3)*q37 + d(2,f(1))**3*f(1)*q1 + d(2,f(1))**
2*d(1,d(2,df(f(1),x)))*q26 + d(2,f(1))**2*d(1,f(1))*f(1)*q3 + d(2,f(1))**2*df(f(
1),x,2)*q31 + d(2,f(1))*d(1,d(2,df(f(1),x,3)))*q42 + d(2,f(1))*d(1,d(2,df(f(1),x
)))*d(1,f(1))*q27 + d(2,f(1))*d(1,d(2,f(1)))*d(1,df(f(1),x))*q16 + d(2,f(1))*d(1
,df(f(1),x,2))*f(1)*q11 + d(2,f(1))*d(1,df(f(1),x))*df(f(1),x)*q22 + d(2,f(1))*d
(1,f(1))**2*f(1)*q2 + d(2,f(1))*d(1,f(1))*df(f(1),x,2)*q32 + d(2,f(1))*df(f(1),x
,4)*q40 + d(1,d(2,df(f(1),x,5)))*q48 + d(1,d(2,df(f(1),x,3)))*d(1,f(1))*q43 + d(
1,d(2,df(f(1),x,2)))*d(1,df(f(1),x))*q38 + d(1,d(2,df(f(1),x)))*d(1,d(2,f(1)))*f
(1)*q47 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x,2))*q30 + d(1,d(2,df(f(1),x)))*d(1,
f(1))**2*q28 + d(1,d(2,df(f(1),x)))*df(f(1),x)*f(1)*q46 + d(1,d(2,f(1)))*d(1,df(
f(1),x,3))*q15 + d(1,d(2,f(1)))*d(1,df(f(1),x))*d(1,f(1))*q17 - d(1,d(2,f(1)))*
df(f(1),x,2)*f(1)*q45 + d(1,df(f(1),x,4))*f(1)*q12 + d(1,df(f(1),x,3))*df(f(1),x
)*q21 + d(1,df(f(1),x,2))*d(1,f(1))*f(1)*q10 + d(1,df(f(1),x,2))*df(f(1),x,2)*
q35 + d(1,df(f(1),x))**2*f(1)*q7 + d(1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q23 + d(
1,df(f(1),x))*df(f(1),x,3)*q36 + d(1,f(1))**3*f(1)*q4 + d(1,f(1))**2*df(f(1),x,2
)*q33 + d(1,f(1))*df(f(1),x,4)*q41 + df(f(1),x,6)*q49 + df(f(1),x,2)*df(f(1),x)*
f(1)*q44$