广义(3+1)维KdV方程的lump解、相互作用解和呼吸子解

于明惠; 王云虎

doi:10.21656/1000-0887.430353

广义(3+1)维KdV方程的lump解、相互作用解和呼吸子解

doi: 10.21656/1000-0887.430353

于明惠,
王云虎^,

上海海事大学理学院，上海 201306

基金项目:

国家自然科学基金项目 12275172

国家自然科学基金项目 11905124

详细信息

作者简介:
于明惠(1997—)，女，硕士生(E-mail: yumingh97@163.com)

通讯作者:
王云虎（1982—）,男，副教授（通讯作者. E-mail： yhwang@ shmtu.edu.cn）

中图分类号: O175.29
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- 文章访问数: 685
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- 被引次数: 0
出版历程
- 收稿日期: 2022-11-04
- 修回日期: 2022-12-18
- 刊出日期: 2023-08-01

Lump Solutions, Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations

YU Minghui,
WANG Yunhu^,

School of Science, Shanghai Maritime University, Shanghai 201306, P.R.China

摘要

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.
- 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.
- generalized (3+1)-dimensional KdV equation /
- lump solution /
- interaction solution /
- breather solution

HTML全文

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)

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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)

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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

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图 4 线孤子产生的“裂变”现象

Figure 4. Fission phenomena produced by the one-stripe soliton

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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

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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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图 7 解(30)的三维图(y-z-v), y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 7. The 3D plot (y-z-v), the y-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

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