
The D'Alembert type waves and the soliton molecules in a (2+1)-dimensional Kadomtsev-Petviashvili with its hierarchy equation
Hui-Ling Wu(吴慧伶),Sheng-Wan Fan(樊盛婉),Jin-Xi Fei(费金喜),Zheng-Yi Ma(马正义)
Communications in Theoretical Physics ›› 2021, Vol. 73 ›› Issue (10) : 105002.
The D'Alembert type waves and the soliton molecules in a (2+1)-dimensional Kadomtsev-Petviashvili with its hierarchy equation
For a one (2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D'Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the Bäcklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.
Kadomtsev-Petviashvili equation / soliton molecule / breather/lump soliton / elastic interaction {{custom_keyword}} /
• | One two-soliton molecule |
Figure 2. (a) The two-soliton molecule structure of the solution v from equations ( |
• | One three-soliton molecule |
• | One four-soliton molecule |
• | The soliton molecule through a line soliton and a lump |
• | The soliton molecule through the line soliton molecule and a lump |
• | The soliton molecule through a line soliton and the breather |
Figure 6. (a) The soliton molecule expressed a line soliton and the breather for the variable v of equation ( |
• | The soliton molecule through the line soliton molecule and the breather |
• | The soliton molecule through two breathers |
1 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
2 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
3 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
4 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
5 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
6 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
7 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
8 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
9 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
10 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
11 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
12 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
13 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
14 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
15 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
16 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
17 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
18 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
19 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
20 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
21 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
22 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
23 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
24 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
25 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
26 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
27 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
28 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
29 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
30 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
31 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
32 |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
{{custom_ref.label}} |
{{custom_citation.content}}
{{custom_citation.annotation}}
|
/
〈 |
|
〉 |