Solusi Soliton On-Site Persamaan Saturable Discrete Nonlinear Schrödinger Menggunakan Metode Newton
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Abstract
The discrete nonlinear Schrödinger equation is a differential equation that describes wave propagation in a discrete lattice. This equation has solutions with very interesting characteristics, namely solitons. Two types of solitons that can be obtained from this differential equation are on-site and inter-site solitons. The equation that is the focus of this study is the discrete nonlinear Schrödinger equation with saturable type nonlinearity. The on-site soliton solution in this study is obtained by substituting an ansatz into the equation to obtain a stationary equation. This stationary equation is then solved using Newton's method. The solution is then analyzed for stability by adding a perturbation term to the solution ansatz. This study aims to find the on-site soliton solution, analyze the effect of coupling parameters, nonlinearity, and trapping potential on the soliton profile, and analyze the stability of each solution obtained by the linear perturbation technique. The results show that variations in the values of the coupling parameters and the given nonlinearity and trapping potential affect the on-site soliton profile, both in terms of profile width and soliton amplitude. All obtained solutions are declared stable based on linear stability analysis.
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References
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