Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation
The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2+1-dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2+1-dimensional Boussinesq equation. By the veloc...
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2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/5545984 |
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| author | Bo Ren |
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| description | The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2+1-dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2+1-dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2+1-dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. This lump wave is just the bright form by some detail analysis. The graphics in this study are carried out by selecting appropriate parameters. The results in this work may enrich the variety of the dynamics of the high-dimensional nonlinear wave field. |
| format | Article |
| id | doaj-art-840e8903eeaa4eab8cbd6934c702f623 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-840e8903eeaa4eab8cbd6934c702f6232025-02-03T01:20:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/55459845545984Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq EquationBo Ren0Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, ChinaThe soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2+1-dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2+1-dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2+1-dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. This lump wave is just the bright form by some detail analysis. The graphics in this study are carried out by selecting appropriate parameters. The results in this work may enrich the variety of the dynamics of the high-dimensional nonlinear wave field.http://dx.doi.org/10.1155/2021/5545984 |
| spellingShingle | Bo Ren Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation Advances in Mathematical Physics |
| title | Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation |
| title_full | Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation |
| title_fullStr | Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation |
| title_full_unstemmed | Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation |
| title_short | Characteristics of the Soliton Molecule and Lump Solution in the 2+1-Dimensional Higher-Order Boussinesq Equation |
| title_sort | characteristics of the soliton molecule and lump solution in the 2 1 dimensional higher order boussinesq equation |
| url | http://dx.doi.org/10.1155/2021/5545984 |
| work_keys_str_mv | AT boren characteristicsofthesolitonmoleculeandlumpsolutioninthe21dimensionalhigherorderboussinesqequation |