| Citation: |
Jinting Ha, Huiqun Zhang, Qiulan Zhao. EXACT SOLUTIONS FOR A DIRAC-TYPE EQUATION WITH N-FOLD DARBOUX TRANSFORMATION[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 200-210. doi: 10.11948/2019.200
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EXACT SOLUTIONS FOR A DIRAC-TYPE EQUATION WITH N-FOLD DARBOUX TRANSFORMATION
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Abstract
Based on matrix spectral problems associated with the real special orthogonal Lie algebra so(3, $\mathbb{R}$), a Dirac-type equation is derived by virtue of the zero-curvature equation. Further, an N-fold Darboux transformation for the Dirac-type equation is constructed by means of the gauge transformation. Finally, as its application, some exact solutions and their figures are obtained via symbolic computation software (Maple). -
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References
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Jinting Ha, Huiqun Zhang, Qiulan Zhao. EXACT SOLUTIONS FOR A DIRAC-TYPE EQUATION WITH N-FOLD DARBOUX TRANSFORMATION[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 200-210. doi: 10.11948/2019.200
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Figure 1. Plots of the intensity distribution
$ \hat p $ and the solution$ \hat p $ at$ t = 0 $ of Eq. (1.1) with$ {\lambda _1} = {\lambda _2} = 1, \ {\lambda _3}{\rm{ = - 1}}, \ \gamma _1^{(2)} = 0, \ \gamma _1^{(1)} = \gamma _3^{(2)} = 1, \ \gamma _2^{(1)} = \gamma _2^{(2)} = \gamma _3^{(1)} = - 1. $ . -
Figure 2. Plots of the intensity distribution
$ \hat q $ and the solution$ \hat q $ at$ t = 0 $ of Eq. (1.1) with$ {\lambda _1} = {\lambda _2} = 1, \ {\lambda _3}{\rm{ = - 1}}, \ \gamma _1^{(2)} = 0, \ \gamma _1^{(1)} = \gamma _3^{(2)} = 1, \ \gamma _2^{(1)} = \gamma _2^{(2)} = \gamma _3^{(1)} = - 1. $ .