Solution 2 to problem N2f1b0o23w3


Expressions | Parameters | Inequalities | Relevance | Back to problem N2f1b0o23w3

Expressions

The solution is given through the following expressions:

q6= - i*q4


q5=q4


q3=i*q4


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:
 q8, q7, q4, 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.
 
{q3,

 q4,

 p3,

 g0005*q7 + g0006*q4 + g0007*q4 + g0008*i*q4 + g0010*p3,

 p4,

 g0012*q7 - g0013*i*q4 + g0014*q4 + g0015*i*q4 + g0017*p3,

 g0027*q8 + g0028*q7 - g0029*i*q4 + g0030*q4 + g0031*q4 + g0032*i*q4}


Relevance for the application:



The equation: 


f =D D f *p3 + f  *i*p3
 t  1 2 x       2x
The symmetry:
f =D f*D D f*i*q4 + D f*f *q4 + D D f  *q7 + D D f*D f*q4 - D f*f *i*q4 + f  *q8
 s  2   1 2          2   x       1 2 2x       1 2   1        1   x         3x
And now in machine readable form:

The system:

df(f(1),t)=d(1,d(2,df(f(1),x)))*p3 + df(f(1),x,2)*i*p3$
The symmetry:
df(f(1),s)=d(2,f(1))*d(1,d(2,f(1)))*i*q4 + d(2,f(1))*df(f(1),x)*q4 + d(1,d(2,df(
f(1),x,2)))*q7 + d(1,d(2,f(1)))*d(1,f(1))*q4 - d(1,f(1))*df(f(1),x)*i*q4 + df(f(
1),x,3)*q8$