Solution 48 to problem e3null

Expressions | Parameters | Relevance | Back to problem e3null

Expressions

The solution is given through the following expressions:


a33=2*a22


b22=0


b31=0


b32=0


b33=0


c12=0


c13=0


c22=0


c23=0


c33=0


n1=0


n2=0


n3=0


m1=0


m3=0


r6=0


r5=0


r4=0


r3=0


r2=0


r1=0


q19=0


q18=0


q17=0


q16=0


q15=0


          2
     k1*m2
q14=--------
         2
      a22


q13=0


q12=0


q11=0


q10=0


         2
    k1*m2
q9=--------
        2
     a22


q8=0


q7=0


q5=0


q4=0


q3=0


q2=0


q1=0


p50=0


p49=0


p48=0


p47=0


p46=0


p45=0


p44=0


p43=0


p42=0


p41=0


p40=0


p39=0


p38=0


p37=0


p36=0


     4*k1*m2
p35=---------
       a22


p34=0


p33=0


p32=0


p31=0


p30=0


p29=0


p28=0


p27=0


p26=0


p25=0


p24=0


p23=0


p22=0


p21=0


p20=0


     2*k1*m2
p19=---------
       a22


p18=0


     2*k1*m2
p17=---------
       a22


p16=0


p15=0


p14=0


p13=0


p12=0


p11=0


p10=0


p9=0


p8=0


p7=0


p6=0


p5=0


p4=0


p3=0


p2=0


p1=0


k104=0


k103=0


k102=0


k101=0


k100=0


k99=0


k98=0


k97=0


k96=0


k95=0


k94=0


k93=0


k92=0


k91=0


k90=0


k89=0


k88=0


k87=0


k86=0


k85=0


k84=0


k83=0


k82=0


k81=0


k80=0


k79=0


k78=0


k77=0


k76=0


k75=0


k74=0


k73=0


k72=0


k71=0


k70=0


k69=0


k68=0


k67=0


k66=0


k65=0


k64=0


k63=0


k62=0


k61=0


k60=0


k59=0


k58=0


k57=0


k56=0


k55=0


k54=0


k53=0


k52=0


k51=0


k50=0


k49=0


k48=0


k47=0


k46=0


k45=0


k44=0


k43=0


k42=0


k41=0


k40=0


k39=0


k38=0


k37=0


k36=0


k35=0


k34=0


k33=0


k32=0


k31=0


k30=0


k29=0


k28=0


k27=0


k26=0


k25=0


k24=0


k23=0


k21=0


k20=0


k19=0


k18=0


k17=0


k16=0


k14=0


k13=0


k12=0


k11=0


k10=0


k9=0


k8=0


k7=0


k6=0


k5=k1


k4=0


k3=2*k1


k2=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:

 k1,m2,a22

Relevance for the application:

The following expression INT is a first

integral for the Hamiltonian HAM:

          2         2           2
HAM=a22*u1  + a22*u2  + 2*a22*u3  + m2*v2

            2   4        2   2   2      2   4              2
INT=(k1*(a22 *u1  + 2*a22 *u1 *u2  + a22 *u2  + 2*a22*m2*u1 *v2

                       2                            2   2     2   2      2
          + 2*a22*m2*u2 *v2 + 4*a22*m2*u2*u3*v3 + m2 *v1  + m2 *v2 ))/a22



And again in machine readable form:



HAM=a22*u1**2 + a22*u2**2 + 2*a22*u3**2 + m2*v2$

INT=(k1*(a22**2*u1**4 + 2*a22**2*u1**2*u2**2 + a22**2*u2**4 + 2*a22*m2*u1**2*v2 
+ 2*a22*m2*u2**2*v2 + 4*a22*m2*u2*u3*v3 + m2**2*v1**2 + m2**2*v2**2))/a22**2$