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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.

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# Coupled differential equation with boundary conditions

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