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

Irvan Maulana, Zulfi Abdullah


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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Agrawal, G. P., Applicaton of Nonlinear Fiber Optic (Academic Pres Inc, San Diego, 2001).

Bao, W., Jaksch, D., Markowich, P. A., Numerical Solution of The Gross-Pitaevski Equation for Bose-Einstein Condensation, Journal Comput. Phys., 186, 318-342 (2003).

Dag, I., A Quadratic b-Spline Finite Element method for Solving Nonlinear Schrödinger, Computer Methods in Applied Mechanics and Engineering, 174, 247-258 (1999).

Debnath, L., Nonlinear Partial Differential Equations (Springer, New York, 2012).

Dehghan, M., Taleei, A., Numerical Solution of Nonlinear Schrödinger Equation by Using Time-Space Pseudo-Spectral Method, Wiley Interscience, 26, 979-992 (2009).

Delfour, M., Fortin, M., Payre, G., Finite Difference Solutions of a Nonlinear Schrödinger Equation, Journal Comput. Physics, 44, 277-288 (1981).

El-Baghdady, G., El-Azab, M.S., Chebyshev-Gauss-Lobatto Pseudo-Spectral Method for One-Dimensional Advection-Diffusion Equation with Variable Coefficients, Sohag Journal Math., 3, 7-14 (2016).

Fordy A.P., Soliton Theory: A Survey Of Result (Manchester University Press, Manchester, (1990).

Harris, D. O., Engerholm, G. G., dan Gwinn, W. D., Calculation of Matrix Elements For One-Dimensional Quantum-Mechanical Problems and the Application to Anharmonic Oscilator, The Journal of Chemical Physics, 43, 1515-1517 (1965).

Stenflo, L., Yu, M. Y., Nonlinear Wave Modulation in a Cylindrical Plasma, IEEE Trans Plasma Sci, 25, 1155-1157 (1997).

Sulem, C., Sulem, P. L., The Nonlinear Schrödinger Equation : Self-Focusing and Wave Collapse (Springer, New York, 1999).

Theodorakopoulos, N., Nonlinear Physics (Konstanz University, German, 2006).

Wadati, M., Introduction to Soliton (University of Tokyo, Tokyo, 2001).

Zhou, Q., Ekici, M., dan Sonmezoglu, A., The Inetigation of Solitons of the Coupled Sine-Gordon Equation in Nonlinear Optics, Journal of Modern Optics, 64, 1677-1682. (2017).



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