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COUPLED NONLOCAL NONLINEAR SCHR?DINGER EQUATION AND N-SOLITON SOLUTION FORMULA WITH DARBOUX TRANSFORMATION 被引量:1

COUPLED NONLOCAL NONLINEAR SCHR?DINGER EQUATION AND N-SOLITON SOLUTION FORMULA WITH DARBOUX TRANSFORMATION
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摘要 Ablowitz and Musslimani proposed some new nonlocal nonlinear integrable equations including the nonlocal integrable nonlinear Schr?dinger equation. In this paper, we investigate the Darboux transformation of coupled nonlocal nonlinear Schr?dinger(CNNLS) equation with a spectral problem. Starting from a special Lax pairs, the CNNLS equation is constructed. Then, we obtain the one-, two-and N-soliton solution formulas of the CNNLS equation with N-fold Darboux transformation. Based on the obtained solutions, the propagation and interaction structures of these multi-solitons are shown, the evolution structures of the one-dark and one-bright solitons are exhibited with N = 1,and the overtaking elastic interactions among the two-dark and two-bright solitons are considered with N = 2. The obtained results are different from those of the solutions of the local nonlinear equations. Some different propagation phenomena can also be produced through manipulating multi-soliton waves.The results in this paper might be helpful for understanding some physical phenomena described in plasmas. Ablowitz and Musslimani proposed some new nonlocal nonlinear integrable equations including the nonlocal integrable nonlinear Schr?dinger equation. In this paper, we investigate the Darboux transformation of coupled nonlocal nonlinear Schr?dinger(CNNLS) equation with a spectral problem. Starting from a special Lax pairs, the CNNLS equation is constructed. Then, we obtain the one-, two-and N-soliton solution formulas of the CNNLS equation with N-fold Darboux transformation. Based on the obtained solutions, the propagation and interaction structures of these multi-solitons are shown, the evolution structures of the one-dark and one-bright solitons are exhibited with N = 1,and the overtaking elastic interactions among the two-dark and two-bright solitons are considered with N = 2. The obtained results are different from those of the solutions of the local nonlinear equations. Some different propagation phenomena can also be produced through manipulating multi-soliton waves.The results in this paper might be helpful for understanding some physical phenomena described in plasmas.
作者 Rui Fan Fajun Yu
出处 《Annals of Applied Mathematics》 2019年第1期47-62,共16页 应用数学年刊(英文版)
基金 supported by the Natural Science Foundation of Liaoning Province(Grant No.201602678)
关键词 COUPLED NONLOCAL NONLINEAR Schrodinger(CNNLS) EQUATION DARBOUX transformation dark SOLITON bright SOLITON coupled nonlocal nonlinear Schrodinger(CNNLS) equation Darboux transformation dark soliton bright soliton
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