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

Irvan Maulana; Zulfi Abdullah

doi:10.25077/jfu.9.1.85-92.2020

Authors

Irvan Maulana Laboratorium Teori dan Nuklir, Jurusan Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas
Zulfi Abdullah Laboratorium Teori dan Nuklir, Jurusan Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas

DOI:

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

Abstract

Analisis solusi persamaan SchrÃ¶dinger 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 SchrÃ¶dinger (CNLS) dan Generalized Nonlinear SchrÃ¶dinger (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.

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Analysis of Nonlinear SchrÃ¶dinger (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 SchrÃ¶dinger (CNLS) and Generalized Nonlinear SchrÃ¶dinger (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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