Aproksimasi Variasional untuk Soliton Onsite pada Persamaan Schrödinger Nonlinier Diskrit Kubik-Kuintik

Riza Asfa, Azzahro Fitri Azadi, Zita Putri Netris, Mahdhivan Syafwan

Abstract


Persamaan Schrödinger nonlinier diskrit (SNLD) kubik-kuintik merupakan persamaan beda-diferensial yang memiliki eksistensi solusi soliton. Pada artikel ini hampiran solusi soliton stasioner dengan konfigurasi bertipe onsite pada persamaan SNLD kubik-kuintik untuk limit anti-continuum ditentukan dengan menggunakan metode aproksimasi variasional (AV). Fungsi penduga yang diusulkan berbentuk eksponensial dengan tiga parameter variasional. Solusi AV yang diperoleh selanjutnya diperiksa validasinya dan dibandingkan dengan solusi numerik. Hasil yang diperoleh menunjukkan bahwa solusi AV valid dan mempunyai kesesuaian yang sangat baik dengan solusi numerik.

Keywords


Persamaan Schrödinger nonlinier diskrit kubik-kuintik; soliton onsite; aproksimasi variasional

Full Text:

PDF

References


P. G. Kevrekidis, “Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives,” Springer Tracts in Modern Physics, Volume 54. Springer, 2009.

J.T. Mendonça dan Hugo Terças, “Physics of Ultra-Cold Matter: Atomic Clouds, Bose-Einstein Condensates and Rydberg Plasmas,” Springer, New York, 2013.

A. Nobel, “The Nobel Prize in Physics 2001,” 2001. [Online]. Available: https://www.nobelprize.org/prizes/physics/2001/advanced-information/. [Accessed: 10-Feb-2018].

P. G. Drazin dan R. S. Johnson, “Soliton: An Introduction,” Cambridge University Press, Cambridge. 1989.

M. J. Ablowitz dan J. F. Ladik, “Nonlinear differential – difference equations and Fourier analysis”, J.Math Phys, vol. 16, pp. 598, 1976.

K. W. Cassel, Variational methods with applications in science and engineering, Cambridge University Press, Cambridge, 2013.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E, vol. 53, no. 1, pp. 1172–1189, 1996.

D. J. Kaup, “Variational solutions for the discrete nonlinear Schrödinger equation,” Math. Comput. Simul., vol. 69, no. 3–4, pp. 322–333, 2005.

J. Cuevas, G. James, P. G. Kevrekidis, B.A. Malomed dan B. Sánchez-Rey, "Approximation of solitons in the discrete NLS equation," J. Nonlinear Math. Phys, vol. 15, pp. 124, 2008.

Syafwan, M., "Variational approximations for solitons in a parametrically driven discrete nonlinear Schrödinger equation," Prosiding Seminar Nasional Matematika dan Pendidikan Matematika. 31 Oktober 2012, Universitas Andalas, Padang, Indonesia. Hal. 52-58, 2012.

Susanto, H, Q. E. Hoq dan P. G. Kevrekidis," Stability of discrete solitons in the presence of parametric driving," Phys. Rev. E. 74: 067601, 2006.

Syafwan, M, H. Susanto dan S. M. Cox.," Discrete solitons in electromechanical resonators," Phys. Rev. E. 81: 026207, 2010.

P. S. Matematika and U. Andalas, “Aproksimasi variasional untuk solusi ¨ soliton pada persamaan schr odinger nonlinier diskrit nonlokal,” vol. 5, no. 3, pp. 40–46.

Syafwan, M, Efendi, N. Arifin, "Variational approximations for twisted solitons in a parametrically driven discrete nonlinear Schrödinger equation". Journal of Physics: Conf. Series 983: 012145, 2018.

C. Chong, D. E. Pelinovsky, and G. Schneider, “On the validity of the variational approximation in discrete nonlinear Schrödinger equations,” Phys. D Nonlinear Phenom., vol. 241, no. 2, pp. 115–124, 2011.

C. Chong and D. E. Pelinovsky, “Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonlinear schrödinger lattices,” Discret. Contin. Dyn. Syst. - Ser. S, vol. 4, no. 5, pp. 1019–1031, 2011.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun., vol. 219, no. 1–6, pp. 427–433, 2003.

C. Chong, R. Carretero-Gonz_alez, B. A. Malomed dan P. G. Kevrekidis, "Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices", Physica D, vol. 238 , 126-136, 2009

D. J. Kaup dan T. K. Vogel, “Quantitative Measurement of Variational Approximations ” Phys. Lett. A , vol. 362, pp. 53–66, 2007.




DOI: http://dx.doi.org/10.12962/limits.v15i2.3878

Refbacks

  • There are currently no refbacks.


Jumlah Kunjungan:

Creative Commons License
Limits: Journal Mathematics and its Aplications by Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/limits.