Abstract:Dynamical behavior of the bright solitons in non-Kerr fiber can be described by the nonlinear Schrodinger equation (NLSE) with cubic-quintic competing nonlinear terms. In this paper, to numerically solve the initial value problem of the NLSE, two difference schemes are proposed. Firstly, we transfer the initial value problem into the initial value problem with boundary conditions, truncate the unbounded region into a bounded region and construct a reasonable boundary condition based on the asymptotic behavior of bright solitons in the far field. Then we design the Crank-Nicolson finite difference (CNFD) and time-splitting finite difference (TSFD) schemes. The CNFD scheme is fully implicit and can conserve the discrete energy and mass. Meanwhile, the TSFD is linear implicit and can only conserve the discrete mass. Finally, after the performance of the two schemes is compared by some examples, we explore the stability and interaction of the bright solitons in non-Kerr fiber by using the TSFD scheme.
