Solution 3 to problem N2f0b1o35w4


Expressions | Parameters | Inequalities | Relevance | Back to problem N2f0b1o35w4

Expressions

The solution is given through the following expressions:

q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q6= - i*q7


q5= - i*q7


q4= - q7


q3=0


q2=0


q1=0


p5=i*p4


p3=0


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:
 q16, q15, q7, 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.
 
{q5,

 q7,

 p4,

 g0003*q15 + g0009*q7 - g0010*i*q7 - g0011*i*q7 + g0014*p4,

 p5,

 g0017*q15 + g0023*q7 - g0024*i*q7 - g0025*i*q7 + g0028*p4,

 g0048*q16 + g0049*q15 + g0057*q7 - g0058*i*q7 - g0059*i*q7 - g0060*q7}


Relevance for the application:



The equation: 


b =D D b  *p4 + b  *i*p4
 t  1 2 2x       3x
The symmetry:
b = - D D b*b  *i*q7 + D D b  *q15 + D D b *D D b*q7 - D D b *b *i*q7 + b  *q16
 s     1 2   2x         1 2 4x        1 2 x  1 2        1 2 x  x         5x

 - b  *b *q7
    2x  x
And now in machine readable form:

The system:

df(b(1),t)=d(1,d(2,df(b(1),x,2)))*p4 + df(b(1),x,3)*i*p4$
The symmetry:
df(b(1),s)= - d(1,d(2,b(1)))*df(b(1),x,2)*i*q7 + d(1,d(2,df(b(1),x,4)))*q15 + d(
1,d(2,df(b(1),x)))*d(1,d(2,b(1)))*q7 - d(1,d(2,df(b(1),x)))*df(b(1),x)*i*q7 + df
(b(1),x,5)*q16 - df(b(1),x,2)*df(b(1),x)*q7$