Localized solutions of extended discrete nonlinear schrödinger equation

• Main Authors: Umarov, Bakhram A., Ismail, Nazmi Hakim, Abdul Hadi, Muhammad Salihi, Hassan, Torla
• Format: Conference or Workshop Item
• Language: English; English
• Published: Institute of Physics Publishing 2017
• Subjects: QA Mathematics; QC Physics
• Online Access: http://irep.iium.edu.my/60318/8/60318_Localized%20solutions%20of%20extended_complete_new.pdf; http://irep.iium.edu.my/60318/9/60318_Localized%20solutions%20of%20extended_scopus.pdf; http://irep.iium.edu.my/60318/; http://iopscience.iop.org/journal/1742-6596

We consider the extended discrete nonlinear SchrÄodinger (EDNLSE) equation which includes the nearest neighbor nonlinear interaction in addition to the on-site cubic and quintic nonlinearities. This equation describes nonlinear excitations in dipolar Bose-Einstein condensate in a periodic optical lattice. We are particularly interested with the existence and stability conditions of localized nonlinear excitations of di®erent types. The problem is tackled numerically, by application of Newton methods and by solving the eigenvalue problem for linearized system near the exact solution. Also the modulational instability of plane wave solution is discussed.