| Citation: |
Asma Issasfa, Ji Lin. LUMP AND MIXED ROGUE-SOLITON SOLUTIONS TO THE 2+1 DIMENSIONAL ABLOWITZ-KAUP-NEWELL-SEGUR EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 314-325. doi: 10.11948/20190160
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LUMP AND MIXED ROGUE-SOLITON SOLUTIONS TO THE 2+1 DIMENSIONAL ABLOWITZ-KAUP-NEWELL-SEGUR EQUATION
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Abstract
In this paper, the 2+1 dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation which obtained from the potential Boiti-Leon-Manna-Pempi nelli (pBLMP) equation, is introduced. Through the bilinear method and ansatz technique, the rational solutions consisting of rogue wave and lump soliton solutions are constructed, where we discuss the condition of guaranteeing the positiveness and analyticity of the lump solutions. The collection of a quadratic function with an exponential function describing rationalexponential solutions is proved, the interaction consisting of one lump and one soliton with fission and fusion phenomena. The second kind of interaction comprises the line rogue wave and soliton solution, which is inelastic. With the usage of the extended homoclinic test approach, the homoclinic breather-wave solution is derived. The characteristics of these various solutions are exhibited and illustrated graphically. -
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References
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Asma Issasfa, Ji Lin. LUMP AND MIXED ROGUE-SOLITON SOLUTIONS TO THE 2+1 DIMENSIONAL ABLOWITZ-KAUP-NEWELL-SEGUR EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 314-325. doi: 10.11948/20190160
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- Figure 1. Lump solution of Eq. (1.1) for case1, with the parameters $ a_3 = \frac{1}{2}, a_4 = 0, a_5=1, a_7 = -1, a_8=3, b_3 = \frac{1}{2}, $ at $t=0$, (a) $|\psi|^2$, (b) Density plot of $|\psi|^2$ at $t=0$
- Figure 2. Lump solution of Eq. (1.1) for case1, with the parameters $a_3 = 1, a_4 = 2, a_5=2, a_7 = -1, a_8=3, b_3 = \frac{1}{2}, $ (a) $\phi$, (b) Density plot of $\phi$ at $t=0$, (c) Contour plots of $\phi$ at $t=-80, t=0, t=80$, (d) $|\psi|^2$, (e) Density plot of $|\psi|^2$ at $t=0$, (f) Contour plots of $|\psi|^2$ at $t=-35, t=0, t=35$
- Figure 3. Perspective view of rational-exponential solution $|\psi|^2$ for Eq. (1.1), with the parameter $a_4=1, a_9=2, a_5=0.25, a_8=5, k_1=1.25 (a) t=-30 (b) t=-6 (c) t=20$, in the $(x, y)$-plane
- Figure 4. Perspective view of rational-exponential solution $|\psi|^2$ for Eq. (1.1), with the parameter $a_4=1, a_9=2, a_5=0.25, a_8=5, k_1=-1 (a) t=-30 (b) t=-10 (c) t=20$, in the $(x, y)$-plane
- Figure 5. $|\psi|^2$ for Eq. (1.1), with the parameter $a_4=0.5, a_9=2, a_8=-1.5, k_1=-1, (a) t=-30 (b) t=0 (c) t=3 (d) t=30$, in the $(x, y)$-plane
- Figure 6. Perspective view of rational-exponential solution $|\psi|^2$ for Eq. (1.1), with the parameter $a_4=1, a_9=2, a_5=0.25, a_8=5, k_1=1.25 (a) t=-30 (b) t=-6 (c) t=20$, in the $(x, y)$-plane
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Figure 7. Perspective view of rational-exponential solution
$ |\psi|^2 $ for Eq. (1.1), with the parameter$ a_4 = 0.5, a_9 = 2, a_8 = -1.5, k_1 = -1, (a) t = -30 (b) t = 0 (c) t = 3 (d) t = 30 $ , in the$ (x, y) $ -plane -
Figure 8. Perspective view of rational-exponential solution
$ \phi $ for Eq. (1.1), with the parameter$ a_4 = 0.5, a_9 = 2, a_8 = -1.5, k_1 = -1, (a) t = -30 (b) t = 0 (c) t = 3 (d) t = 30 $ , in the$ (x, y) $ -plane - Figure 9. Periodic solitary-wave solution for $|\psi|^2$ of Eq. (1.1), with the parameters $ P=1, P_1=-1.5, b_0=-2, $ at $t=1$, (a) plot $|\psi|^2$, (b) Contour plot of $|\psi|^2$ at $t=-10, t=0, t=10$
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Figure 10. Kinky periodic-wave solution for
$ \phi $ of Eq. (1.1), with the parameters$ P = 1, P_1 = -1.5, b_0 = -2, $ at$ t = 1 $ , (a) plot of$ \phi $ , (b) Density plot of$ \phi $