High intensity laser beam transmitting in medium can result in amusing phenomena because of the nonlinear interaction between the laser pulse and the medium.Optical soliton is the just due to the balance between the medium responding nonlinearly to the intensity laser and the diffraction of the intensity laser beam

which have been a subject of many studies.The model for discussing optical soliton is nonlinear Schdinger equation(NLS)

which is derived from Maxwell’s equations.The optical soliton

according to transverse coordinate and transmitting direction

can be divided into(

n

+1)D(

n

=1

2

3) spatial optical soliton that have

n

dimensions transverse coordinate and one transmitting direction.(2+1)D optical soliton modes are studied in this paper.Starting from nonlinear Schdinger equation(NLS)

the condition that the(2+1)D spatial optical soliton in saturable nonlinear medium would be exist or not

and the boundary conditions for numerically calculating the modes were discussed by mathematical analysis method.By numerical analysis

the base-mode and one-order modes were given by pretty figures including slowly varying beam envelope

beam intensity and three-dimension distribution of beam intensity

and the powers of each soliton were given(a.u.).The results indicate that the soliton is not arbitrary but depending on power

for example

if the beam power would not equal to soliton power

the soliton do not exist.This conclusion could be evidenced further in this paper

if setting the fitting starting value(equivalent to power of optical beam)

the solution of Schdinger equation are existence

and if starting value is unfitting

then the solution behave surge

none solution.Meanwhile

the influence of the medium saturable nonlinear parameter and wave vector

which is the soliton transmitting in the direction of

z

are studied.The results show that if the

k

m

n is fixed on

the power is increasing with α becoming bigger.And if the α

m

n is fixed on

the location of biggest power shift to the position with small r value.The conclusions of this paper shows that the soliton has internal structure

and have the instructive action for the soliton researching.