Solitary wave analysis of the Kadomtsev–Petviashvili model in mathematical physics

Figures & data

Figure 1. Soliton of ${u_1}_{11}(x,y,z)$ for $k=10,\mathrm{ }l=4,m=4,\sigma =0.1.$

Figure 2. Soliton of ${u_1}_{11}(x,y,z)$ for $k=10, l=4,m=4,\sigma =0.01.$

Figure 3. Soliton of ${u_1}_{11}(x,y,z)$ for (a) $k=1, l=4,m=4,\sigma =0.01$ (b) $k=1, l=4,m=4,\sigma =1.$

Figure 4. Wave profile of ${u_1}_{12}(x,y,t)$ for $k=0.001, l=4,m=4,\sigma =0.001.$

Figure 5. Wave profile of ${u_1}_{12}(x,y,t)$ for $k=2, l=4,m=4,\sigma =0.01.$

Figure 6. Wave profile of ${u_1}_{12}(x,y,t)$ for $k=1, l=4,m=4,\sigma =1.$

Figure 7. Wave profile of ${u_1}_{12}(x,y,t)$ for $k=200, l=4,m=4,\sigma =0.01.$

Table 1. Comparison between Yue et al. (2020) solutions and the obtained solutions obtained in this article.

SL	Solution by Yue et al. (2020)	Solution in this article
(i)	For $\delta =\frac{\rho }{2}=3,$ solution ${\psi }_{34}$ becomes $\frac{2}{3}-2{\tan }^2(10t+x+y+z)$	For $k=l=m=1, r=\sqrt{3}, q=2$ and $p=\frac{2}{\sqrt{3}},$ solution $u_{33}$ becomes $\frac{2}{3}-2{\tan }^2(10t+x+y+z)$
(ii)	For $\delta =\frac{\rho }{2}=3,$ solution ${\psi }_{30}$ becomes $-2\mathrm{se}{\mathrm{c}}^2 (10t+x+y+z)$	For $k=l=m=1, r=1, q=0$ and $p=1,$ solution $u_{9_1}$ becomes $-2\mathrm{se}{\mathrm{c}}^2 (10t+x+y+z)$

Yue, C., Khater, M. M., Attia, R. A., & Lu, D. (2020). Computational simulations of the couple Boiti–Leon–Pempinelli (BLP) system and the (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation. AIP Advances, 10(4), 045216. doi:10.1063/1.5142796

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Data availability statement

No real data used here.