In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically. Two numerical methods are derived using the explicit Runge-Kutta method of order four and the linear multistep method (Predictor-Correc...In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically. Two numerical methods are derived using the explicit Runge-Kutta method of order four and the linear multistep method (Predictor-Corrector method of fourth order). The resulting schemes of fourth order accuracy in spatial and temporal directions. The CNSE is non-integrable and has two kinds of soliton solutions: bright and dark soliton. The exact solutions and the conserved quantities of CNSE are used to display the efficiency and robustness of the numerical methods we derived. Interaction of two bright solitons for different parameters is also displayed.展开更多
Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations submit various critical physical phenomena with a typical equation for optical fibres with ...Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations. Many methods used to solve coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.展开更多
In this work, we will derive a numerical method of sixth order in space and second order in time for solving 3-coupled nonlinear Schr<span style="white-space:nowrap;"><span style="white-space:n...In this work, we will derive a numerical method of sixth order in space and second order in time for solving 3-coupled nonlinear Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger 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.展开更多
文摘In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically. Two numerical methods are derived using the explicit Runge-Kutta method of order four and the linear multistep method (Predictor-Corrector method of fourth order). The resulting schemes of fourth order accuracy in spatial and temporal directions. The CNSE is non-integrable and has two kinds of soliton solutions: bright and dark soliton. The exact solutions and the conserved quantities of CNSE are used to display the efficiency and robustness of the numerical methods we derived. Interaction of two bright solitons for different parameters is also displayed.
文摘Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations. Many methods used to solve coupled nonlinear Schr<span style="white-space:nowrap;">ö</span>dinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.
文摘In this work, we will derive a numerical method of sixth order in space and second order in time for solving 3-coupled nonlinear Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger 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.
