Solution 2 to problem N2f1b0o35w5


Expressions | Parameters | Inequalities | Relevance | Back to problem N2f1b0o35w5

Expressions

The solution is given through the following expressions:

q10=q5


q9=i*q5


q8=i*q5


q7= - q5


q6=i*q5


q4= - q5


q3=i*q5


q2=0


q1=0


p4=i*p3


p2=0


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:
 q12, q11, q5, p3

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.
 
{q4,

 q5,

 p3,

 g0005*q11 + g0006*i*q5 + g0007*i*q5 - g0008*q5 + g0009*i*q5 - g0010*q5

  + g0011*i*q5 + g0013*p3,

 p4,

 g0015*q11 + g0016*q5 + g0017*i*q5 - g0018*q5 + g0019*q5 - g0020*q5 + g0021*i*q5

  + g0023*p3,

 g0037*q12 + g0038*q11 + g0039*q5 + g0040*i*q5 + g0041*i*q5 - g0042*q5

  + g0043*i*q5 + g0044*q5 - g0045*q5 + g0046*i*q5}


Relevance for the application:



The equation: 


f =D D f  *p3 + f  *i*p3
 t  1 2 2x       3x
The symmetry:
f = - D f *D D f*q5 + D f *f *i*q5 - D f*D D f *q5 + D f*f  *i*q5 + D D f  *q11
 s     2 x  1 2        2 x  x         2   1 2 x       2   2x         1 2 4x

 + D D f *D f*i*q5 + D D f*D f *i*q5 + D f *f *q5 + D f*f  *q5 + f  *q12
    1 2 x  1          1 2   1 x         1 x  x       1   2x       5x
And now in machine readable form:

The system:

df(f(1),t)=d(1,d(2,df(f(1),x,2)))*p3 + df(f(1),x,3)*i*p3$
The symmetry:
df(f(1),s)= - d(2,df(f(1),x))*d(1,d(2,f(1)))*q5 + d(2,df(f(1),x))*df(f(1),x)*i*
q5 - d(2,f(1))*d(1,d(2,df(f(1),x)))*q5 + d(2,f(1))*df(f(1),x,2)*i*q5 + d(1,d(2,
df(f(1),x,4)))*q11 + d(1,d(2,df(f(1),x)))*d(1,f(1))*i*q5 + d(1,d(2,f(1)))*d(1,df
(f(1),x))*i*q5 + d(1,df(f(1),x))*df(f(1),x)*q5 + d(1,f(1))*df(f(1),x,2)*q5 + df(
f(1),x,5)*q12$