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Localized analytical matter-wave solutions and numerically stabilities of generalized Gross-Pitaevskii(GP(p,q)) equation with three kinds of specific external potentials​

2018-06-10
 

Academic Report

Title: Localized analytical matter-wave solutions and numerically stabilities of generalized Gross-Pitaevskii(GP(p,q)) equation with three kinds of specific external potentials

Reporter: A.Prof. YU Fajun(School of mathematics, Shenyang Normal University)

Time: June 11, 2018 (Monday) AM 10:00-11:00

Location: A1101# room, Innovation Park Building

Contact: Prof. WANG Zhen (Email:wangzhen@dlut.edu.cn)

Abstract: We present the generalized Gross-Pitaevskii (GP(p,q)) equation with three kinds of specific space-time modulated potentials, including a harmonic potential, the gener- alized Rosen-Morse potential, the combination of harmonic and Gaussian(harmonic- Gaussian) potential. Some analytical bright soliton solutions are derived from the generalized GP(p,q) equation via the complex similarity transformation and the generalized stationary nonlinear Schro ̈dinger(NLS) equation. The soliton solutions can be reduced to Jacobi elliptic and spikon-like solutions by choosing the different parameters, and describe some physically relevant phenomena. Furthermore, some stabilities of the obtained matter-wave solutions are addressed numerically. We find that some solutions are stable and can be observed over a broad range of parameters through analyzing the effect of the phase noise and amplitude noise on these solutions. The obtained results may give a certain theoretical guiding significance of relative experiments in Bose-Einstein condensates.

The brief introduction to the reporter: Yu Fajun received his doctorate degree from Applied Mathematics Department of Dalian University of Technology in 2007. His research field is the integrability and analytic solution of nonlinear waves. He published more than 40 papers in "Physical Review E", "Nonlinear Dynamics", "Journal of Mathematical Physics", "Nonlinear Analysis" and other international SCI periodicals, all of which were retrieved by SCI, including 9 articles in SCI1 and 160 times by SCI and these papers was quoted by SCI more than 160 times. He chaired the Youth Fund of National Natural Science Foundation, Doctorate project and province departmental level topic 7 items. In 2011, he was selected for the development plan of the outstanding young scholars in Liaoning province. In 2017, he was selected as the "Hundreds of millions oftalents project" in Liaoning province. In 2018, he was selected as the "top talent" of the high-level talents in Shenyang.