Penyebaran soliton bagi persamaan Persamaan Kubik-Quintik Schrödinger Tak Linear terhadap potensi luar = The soliton scattering of the Cubic-Quintic Nonlinear Schrödinger Equation on the external potentials

• Main Authors: Aklana , Nor Amirah Busul, Umarov, Bakhram
• Format: Conference or Workshop Item
• Language: English; English
• Published: AIP Publishing LLC 2014
• Subjects: QA Mathematics; QC Physics
• Online Access: http://irep.iium.edu.my/39994/6/SKSM22.pdf; http://irep.iium.edu.my/39994/10/39994.pdf; http://irep.iium.edu.my/39994/; http://sksm22.um.edu.my/SKSM22

Persamaan Kubik-Quintik Schrödinger Tak Linear adalah salah satu model matematik sejagat yang menghuraikan banyak permasalahan menarik dalam bidang fizik seperti fizik plasma, bahan fizik pekat, tekanan Bose–Einstein, optik tak linear dan lain-lain. Kertas kajian ini membincangkan penyebaran soliton bagi persamaan kubik-quintik Schrödinger tak linear terhadap potensi luar setempat. Kami telah mempraktikkan kaedah analisis anggaran, iaitu kaedah variasional untuk menerbitkan persamaan bagi evolusi parameter soliton semasa proses penyebaran. Kesahihan anggaran ini kemudiannya diuji oleh simulasi berangka langsung persamaan kubik-quintik Schrödinger tak linear dengan soliton yang pada mulanya terletak jauh dari potensi. Bagi kes potensi dalam bentuk fungsi Gaussian yang bergantung kepada halaju awal soliton, telah menunjukkan soliton berkemungkinan terpantul apabila bertembung dengan potensi, atau bergerak melepasinya. Nilai kritikal halaju yang memisahkan kedua-dua senario tersebut telah dikenal pasti. The Cubic-Quintic Nonlinear Schrödinger Equation (CQNLSE) is one of the universal mathematical models constituting many interesting problems in physics such as plasma physics, condensed matter physics, Bose–Einstein condensates, nonlinear optics, etc. This paper studies the scattering of the soliton of the CQNLSE on the localized external potential namely Gaussian potential. The approximate analytical method, also known as variational method has been applied in order to derive the equations for soliton parameters evolution during the scattering process. The validity of approximations was tested by direct numerical simulations of CQNLSE with soliton initially located far from potential. It was shown, in case of the potential in the form of Gaussian function, that depending on initial velocity of the soliton, the soliton may be reflected by potential or transmitted through it. The critical values of the velocity separating these two scenarios have been identified.