Stability and interaction of bright solitons in non-Kerr fiber
Dynamical behaviors of bright solitons can be described by the nonlinear Schrödinger equation(NLSE)with cubic-quintic competing nonlinear terms.In this paper,to numerically solve the initial val-ue 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 constructe a reasonable boundary condition based on the asymptotic behaviors of bright solitons in the far field.Then we design the Crank-Nicolson finite difference(CNFD)and time-splitting finite difference(TSFD).The CNFD scheme is fully implicit and can conserve discrete energy and mass.Meanwhile,the TSFD scheme is linear implicit and can only conserve discrete mass.Finally,after the performance of the two schemes is compared by some examples,we explore the stability and in-teraction of bright solitons by using the TSFD scheme.
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