Lump Solutions, Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations
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摘要: 基于广义(3+1)维KdV方程的双线性形式，得到了方程的lump解、相互作用解及呼吸子解.证明了lump解在空间各个方向上都是有理局域的，并在lump波与线孤子的相互作用过程中观察到了“聚变”和“裂变”现象，最后得到了方程的呼吸子解.
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关键词:
- 广义(3+1)维KdV方程 /
- lump解 /
- 相互作用解 /
- 呼吸子解
Abstract: Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the "fusion" and "fission" phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained. -
图 1 Lump解(18)的三维图和密度图(y=0, t=0)
Figure 1. The 3D plot and the density plot with lump solutions (18)(y=0, t=0)
图 2 取参数α=γ=δ=a5=a6=1，β=-1，a1=a2=a7=a9=2，a3=5，a10=18时，lump解(13)的三维图和密度图(x=0, t=0)
Figure 2. The 3D plot and the density plot with lump solutions (13) under parameters selected as α=γ=δ=a5=a6=1, β=-1, a1=a2=a7=a9=2, a3=5, a10=18 (x=0, t=0)
图 3 Lump波与线孤子产生的“聚变”现象
Figure 3. Fusion phenomena between the lump wave and the one-stripe soliton
图 5 解(30)的三维图(x-y-v)，x曲线图和密度图，参数取值为α=γ=c5=c7=1, β=-2, c3=0, c2=k1=k3=3, k2=2
Figure 5. The 3D plot (x-y-v), the x-curve plot and the density plot of solution(30) with α=γ=c5=c7=1, β=-2, c3=0, c2=k1=k3=3, k2=2
图 6 解(30)的三维图(x-z-v), z曲线图和密度图，参数取值为α=γ=c2=c5=c7=1, β=-2, c3=0, k1=k2=k3=2
Figure 6. The 3D plot (x-z-v), the z-curve plot and the density plot of solution(30) with α=γ=c2=c5=c7=1, β=-2, c3=0, k1=k2=k3=2
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