Abstract
In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrodinger equations using finite difference method and time splitting method combined with finite difference method. The resulting schemes are highly accurate, unconditionally stable. We use the exact single soliton solution and the conserved quantities to check the accuracy and the efficiency of the proposed schemes. Also, we use these methods to study the interaction dynamics of two solitons. It is found that both elastic and inelastic collision can take place under suitable parametric conditions. We have noticed that the inelastic collision of single solitons occurs in two different manners: enhancement or suppression of the amplitude.
Highlights
In recent years, the concept of soliton has been receiving considerable attention in optical communications, since soliton is capable of propagating over long distances without change of shape and velocity
We will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method
It has been found that the soliton propagating through optical fiber arrays is governed by a set of equations related to the coupled nonlinear Schrödinger equation [1] [2]
Summary
The concept of soliton has been receiving considerable attention in optical communications, since soliton is capable of propagating over long distances without change of shape and velocity. The homogenous boundary conditions q j ( xL ,=t ) q j ( xR ,=t ) 0= , j 1, 2, 3, The exact solution of the 3-coupled nonlinear Schrödinger equation [1] [2] is given by. Many numerical methods for solving the coupled nonlinear Schrödinger equation are derived in the last two decades. A higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equation is given in [13]. A semi-explicit multi-sypmlectic splitting scheme for 3-coupled nonlinear Schrödinger equation is given in [14].
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