| Citation: |
Jian-Guo Liu, Abdul-Majid Wazwaz, Run-Fa Zhang, Zhong-Zhou Lan, Wen-Hui Zhu. BREATHER-WAVE, MULTI-WAVE AND INTERACTION SOLUTIONS FOR THE (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2426-2440. doi: 10.11948/20210507
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BREATHER-WAVE, MULTI-WAVE AND INTERACTION SOLUTIONS FOR THE (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION
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Abstract
In this paper, a (3+1)-dimensional generalized breaking soliton equation in nonlinear media is investigated. The interaction solution between lump wave and N-soliton (N=2, 3, 4) are derived. The interaction solution between lump wave and periodic waves is also studied. Breather-wave and multi-wave solutions are obtained. The dynamical behavior is demonstrated by some 3D graphics and density plots. Via means of mathematical induction, we also obtain the exact solution containing three arbitrary functions.
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References
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Jian-Guo Liu, Abdul-Majid Wazwaz, Run-Fa Zhang, Zhong-Zhou Lan, Wen-Hui Zhu. BREATHER-WAVE, MULTI-WAVE AND INTERACTION SOLUTIONS FOR THE (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2426-2440. doi: 10.11948/20210507
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Figure 1.
$ \mathcal{G}_1= \mathcal{G}_5= \mathcal{G}_{11}=\alpha=a_1=d_1=d_2=e_1=k_1=k_2=1 $ ,$ \mathcal{G}_4=\mathcal{G}_9=-1 $ ,$ \mathcal{G}_6=-3 $ ,$ \beta=3 $ ,$ \mathcal{G}_{10}=a_2=k_{12}=-2 $ ,$ e_2=2 $ ,$ y=0 $ , when$ x=-10 $ in (a) (d),$ x=0 $ in (b) (e),$ x=10 $ in (c) (f). -
Figure 2.
$ \mathcal{G}_1= \mathcal{G}_5= \mathcal{G}_{11}=\alpha=a_1=d_1=d_2=e_1=k_1=k_2=1 $ ,$ \mathcal{G}_4=\mathcal{G}_9=-1 $ ,$ \mathcal{G}_6=-3 $ ,$ \beta=3 $ ,$ \mathcal{G}_{10} =a_2=-2 $ ,$ e_2=2 $ ,$ y=k_{12}=0 $ , when$ x=-10 $ in (a) (d),$ x=0 $ in (b) (e),$ x=10 $ in (c) (f). -
Figure 3.
$ \mathcal{G}_1= \mathcal{G}_5= \mathcal{G}_{11}=\alpha=a_1=d_1=d_2=e_1=1 $ ,$ k_1=e_3=4 $ ,$ \mathcal{G}_{10} =-2 $ ,$ \mathcal{G}_4=\mathcal{G}_9=-1 $ ,$ \mathcal{G}_6=d_3=-3 $ ,$ \beta=a_3=k_3=3 $ ,$ a_2=e_2=k_2=2 $ ,$ y=0 $ , when$ x=-5 $ in (a) (d),$ x=0 $ in (b) (e),$ x=5 $ in (c) (f). -
Figure 4.
$ \mathcal{G}_1= \mathcal{G}_5= \mathcal{G}_{11}=\alpha=a_1=d_1=d_2=e_1=1 $ ,$ k_1=e_3=4 $ ,$ k_4=6 $ ,$ y=0 $ ,$ a_2=e_2=k_2=2 $ ,$ \mathcal{G}_4=\mathcal{G}_9=e_4=-1 $ ,$ \mathcal{G}_6=d_3=d_4=-3 $ ,$ \beta=a_3=k_3=3 $ ,$ \mathcal{G}_{10} =a_4=-2 $ , when$ x=-5 $ in (a) (d),$ x=0 $ in (b) (e),$ x=5 $ in (c) (f). -
Figure 5.
$ \mathcal{G}_1= \mathcal{G}_5= \alpha=a_1=d_1=d_2=e_1=1 $ ,$ \mathcal{G}_{11}=10 $ ,$ \mathcal{G}_4=\mathcal{G}_9=-1 $ ,$ \mathcal{G}_6=-3 $ ,$ \beta=3 $ ,$ \mathcal{G}_{10} =a_2=-2 $ ,$ e_2=k_1=2 $ ,$ k_2=6 $ ,$ y=0 $ , when$ x=-5 $ in (a) (d),$ x=0 $ in (b) (e),$ x=5 $ in (c) (f). -
Figure 6.
$ k_1=d_4=-1 $ ,$ a_1=\alpha=a_2=d_2=d_3=1 $ ,$ \beta=3 $ ,$ a_3=-2 $ ,$ k_2=-6 $ ,$ k_3=2 $ ,$ x=y=0 $ . -
Figure 7.
$ k_1=k_2=k_3=a_1=\alpha=a_1=d_1=d_2=e_1=1 $ ,$ \beta=a_3=3 $ ,$ e_3=4 $ ,$ a_2=e_2=2 $ ,$ d_3=-3 $ ,$ x=y=0 $ . -
Figure 8.
$ k_1=a_1=\alpha=a_1=d_1=d_2=e_1=1 $ ,$ \beta=a_3=3 $ ,$ d_3=-3 $ ,$ e_3=4 $ ,$ a_2=e_2=k_2=2 $ ,$ x=y=k_3=0 $ . -
Figure 9.
$ k_1=k_2=k_3=a_1=\alpha=a_1=d_1=d_2=e_1=1 $ ,$ \beta=a_3=3 $ ,$ e_3=4 $ ,$ a_2=e_2=2 $ ,$ d_3=-3 $ ,$ y=0 $ , when$ x=-5 $ in (a) (d),$ x=0 $ in (b) (e),$ x=5 $ in (c) (f).