Question: How to remove quadratic singularity in dynamical system of coupled ODEs?

I am trying to find the phase portraits of a dynamical system; couples ODE system but it appears in singular form. How can we remove the singularity of coupled ODE system in P and W depending on \xi, where \alpha is scalar and v is velocity.

How remove quadratic singularity to make this system Hamiltonian in below coupled ODE system in P & W.

 singular_system.mw

restart

with(PDEtools):

alias(P = P(xi), W = W(xi))

P, W

(1)

rf1 := diff(P, xi) = W

diff(P, xi) = W

(2)

rf2 := diff(W, xi) = (P-(alpha^2+1)*P*W^2)/(v+(1/2*(alpha^2+1))*P^2)

diff(W, xi) = (P-(alpha^2+1)*P*W^2)/(v+(1/2)*(alpha^2+1)*P^2)

(3)
 

 

Download singular_system.mw

Please Wait...