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Conservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity |
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| Authors: | Shou-Fu Tian Li ZouQi Ding Hong-Qing Zhang |
| Institution: | a School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China b Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2 c School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, People’s Republic of China |
| Abstract: | In this paper, we consider a general form of nonlinear Schrödinger equation with time-dependent nonlinearity. Based on the linear eigenvalue problem, the complete integrability of such nonlinear Schrödinger equation is identified by admitting an infinite number of conservation laws. Using the Darboux transformation method, we obtain some explicit bright multi-soliton solutions in a recursive manner. The propagation characteristic of solitons and their interactions under the periodic plane wave background are discussed. Finally, the modulational instability of solutions is analyzed in the presence of small perturbation. |
| Keywords: | Exact solution Bright matter wave soliton Conservation law Modulational instability Nonlinear Schrö dinger equation with time-dependent nonlinearity |
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