| Citation: |
Hong-Yi Zhang, Yu-Feng Zhang. DARBOUX TRANSFORMATIONS, MULTISOLITONS, BREATHER AND ROGUE WAVE SOLUTIONS FOR A HIGHER-ORDER DISPERSIVE NONLINEAR SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 892-902. doi: 10.11948/20200080
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DARBOUX TRANSFORMATIONS, MULTISOLITONS, BREATHER AND ROGUE WAVE SOLUTIONS FOR A HIGHER-ORDER DISPERSIVE NONLINEAR SCHRÖDINGER EQUATION
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Abstract
In this paper, dynamic of a higher-order dispersive nonlinear Schrö-dinger equation is investigated. Firstly, we obtain the determinant representation of the N-fold Darboux transformations of the Schrödinger equation. Then based on the above analysis, we get the one-soliton, two-soliton and the breather wave solution. Furthermore, the first-order rogue wave is derived by means of a Taylor expansion of the breather wave. Finally, by selecting some special parameters and drawing the 3-D and 2-D graphs to better describe the dynamic traits of those solutions.
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References
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Hong-Yi Zhang, Yu-Feng Zhang. DARBOUX TRANSFORMATIONS, MULTISOLITONS, BREATHER AND ROGUE WAVE SOLUTIONS FOR A HIGHER-ORDER DISPERSIVE NONLINEAR SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 892-902. doi: 10.11948/20200080
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Figure 1. The one-soliton solution of the higher-order dispersive nonlinear Schrödinger equation with
$ \eta = 0.1,\xi = 0.05 $ and$ \tau = 1 $ : a three-dimensional plot, b density plot, c the two-dimensional plot at different$ t = -10 $ (left),$ t = 0 $ (middle),$ t = 10 $ (right). -
Figure 2. The two-soliton solution of the higher-order dispersive nonlinear Schrödinger equation with
$ \eta = 1,\xi = 1,\upsilon = 1,\theta = 0, $ and$ \tau = 1 $ : a three-dimensional plot, b density plot, c the contour plot. -
Figure 3. The first-order breather solution of higher-order dispersive nonlinear Schrödinger equation with
$ \eta = 0.2,\xi = 0,b = 1,c = 1, $ and$ \tau = 1 $ : a three-dimensional plot, b density plot, c the contour plot. -
Figure 4. The first-order rogue wave solution of higher-order dispersive nonlinear Schrödinger equation with
$ \xi = 0,\eta = 0.5,a = 0,b = 1,c = 0.5, $ and$ \tau = 0.5 $ : a three-dimensional plot, b density plot, c the contour plot.