Abstract
In this work, we will derive a numerical method of sixth order in space and second order in time for solving 3-coupled nonlinear Schrödinger equations. The numerical method is 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 study the interaction dynamics of two solitons. It is found that both elastic and inelastic collisions can take place under suitable parametric conditions.
Highlights
In recent years the concept of soliton has been receiving considerable attention in optical communications
We will derive a numerical method of sixth order in space and second order in time for solving 3-coupled nonlinear Schrödinger equations
Since soliton is capable of propagating over long distances without change of shape and velocity, 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] [3]
Summary
In recent years the concept of soliton has been receiving considerable attention in optical communications. The exact soliton solution of the 3-coupled nonlinear Schrödinger equation [2] [3], is given by. The proposed system is of physical interest, in optical communication, and in biophysics This system can be used to study the lunching and propagation of solitons along the three spines of an alpha-helix shape changing in protein [1]. Many numerical methods for solving the coupled nonlinear Schrödinger equation are derived in the last two decades. Proposition 1: The three coupled nonlinear Schrödinger equations have the conserved quantities. The exact values of the conserved quantities using the exact soliton solution (7) are given by the following formula. Fixed point method is used to do this job, and this will be discussed later
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