Analisis Solusi Spatial dan Temporal Persamaan NLS (Nonlinear Schrödinger) Sebagai Solusi Soliton Menggunakan Metode DVR (Discrete Variable Representation

Irvan Maulana, Zulfi Abdullah

Abstract


Analisis solusi persamaan Schrödinger Nonlinear (NLS) dengan menggunakan metode Representasi Variabel Diskrit (DVR) telah dilakukan. Penggunaan metode DVR ini dilakukan dengan mengkontruksikan fungsi basis melalui interpolasi Lagrange dan koefisien spektral yang berdasarkan polinomial Chebyshey pada titik Chebyshev-Gauss-Lobatto (CGL). Hasil simulasi dari metode DVR ini memiliki bentuk yang sama dengan 2 jenis solusi eksak persamaan NLS yaitu Cubic Nonlinear Schrödinger (CNLS) dan Generalized Nonlinear Schrödinger (GNLS), namun memiliki rentang penjalaran yang berbeda. Perbedaan rentang tersebut dikarenakan adanya kondisi awal yang ditetapkan pada metode DVR ini. Penggunaan metode DVR pada pengkondisian CNLS menghasilkan bentuk soliton onsite, sedangkan pada pengkondisian GNLS dihasilkan bentuk soliton onsite namun memiliki amplitudo yang berbeda pada setiap perubahan posisi dan waktu.

 

Analysis of Nonlinear Schrödinger (NLS) equation by using Discrete Variable Representation (DVR) method has been carried out. The DVR method done with built basic function from Lagrange interpolation and spectral coefficient from Chebyshev polynomial in Chebyshev-Gauss-Lobatto (CGL) point. The result of DVR method simulation has same form with 2 type of exact solution of NLS equation are Cubic Nonlinear Schrödinger (CNLS) and Generalized Nonlinear Schrödinger (GNLS), however the result has different distance of propagation. That difference distance caused by initial condition which set on this method. The using of DVR method in CLNS condition produce soliton onsite form, but for GNLS condition produce soliton onsite form too but it has different amplitude for every change of position and time.


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DOI: https://doi.org/10.25077/jfu.9.1.85-92.2020

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