- #1
Shahrokh
- 5
- 1
Hi,
I have two coupled differential equations
d^2 phi(z)/dz^2=lambda*phi(z)*(phi(z)^2+psi(z)^2-sigma^2)
d^2 psi(z)/dz^2=lambda*psi(z)*(phi(z)^2+psi(z)^2-sigma^2+epsilon/lambda)
where lambda, epsilon and sigma are arbitrary constants. The equation subject to the bellow boundary conditions
phi(0)=0, phi(infinity)=sigma, psi(infinity)=0,
I couldn't find any analytical solution but how can I solve them numerically, if I use infinity as the initial point then the answer is the trivial phi(z)=sigma and psi(z)=0 which doesn't satisfy the third boundary condition but I know that this equation must has a solution since a non differential solution is already at my disposal . Thanks.
I have two coupled differential equations
d^2 phi(z)/dz^2=lambda*phi(z)*(phi(z)^2+psi(z)^2-sigma^2)
d^2 psi(z)/dz^2=lambda*psi(z)*(phi(z)^2+psi(z)^2-sigma^2+epsilon/lambda)
where lambda, epsilon and sigma are arbitrary constants. The equation subject to the bellow boundary conditions
phi(0)=0, phi(infinity)=sigma, psi(infinity)=0,
I couldn't find any analytical solution but how can I solve them numerically, if I use infinity as the initial point then the answer is the trivial phi(z)=sigma and psi(z)=0 which doesn't satisfy the third boundary condition but I know that this equation must has a solution since a non differential solution is already at my disposal . Thanks.