ABSTRACT
Laser is the carrier of strong energy with the excellent directivity and stability. People are interested in the formation of soliton. In view of it’s special properties, laser plays an important role in modern science and technology. The intensity (E ) of the electric field in the emission of laser satisfies the nonlinear Schrodinger equation
K z v t
E E
x E
y K
K E t
K n n
E E
2i ( 1
)
2 | | 0
ω
∂ ∂ +
∂ ∂ +
∂ ∂ +
∂ ∂ -
∂ ∂
∂ ∂
+ =
(1)
It changes to (2) with the 2-order ordinary differential problem with singular coefficients through evolution and by using the special solution U = U(ρ) exp(iβζ)
(2)
According to (Lv et al. 2004), it’s electric field intensity satisfies nonlinear Schrodinger equation in the laser emission mechanism, which can be reduced to singular differential equation. And nonlinear Schrodinger equation is an important model in physics. Hence, the problem can be transformed into solving the second-order singular nonlinear differential equations with initial value condition.
