Alternative solitons in the Hirota–Satsuma system via the direct method
Multisolitons and multi-hump solitons are constructed for the coupled Korteweg–de Vries (cKdV) system introduced by Hirota and Satsuma (1981) in the context of the propagation of two waves interacting with different dispersion relations. The direct method analytically exhibit a new class of compleme...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818120300206 |
| _version_ | 1818865271220207616 |
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| author | Hugo Parra Prado Luis A. Cisneros-Ake |
| author_facet | Hugo Parra Prado Luis A. Cisneros-Ake |
| author_sort | Hugo Parra Prado |
| collection | DOAJ |
| description | Multisolitons and multi-hump solitons are constructed for the coupled Korteweg–de Vries (cKdV) system introduced by Hirota and Satsuma (1981) in the context of the propagation of two waves interacting with different dispersion relations. The direct method analytically exhibit a new class of complementary or alternative soliton solutions functionally different to the traditional or classical multisolitons known (Hirota and Satsuma, 1981; Ramani et al., 1983; Parra Prado and Cisneros-Ake, 2020). As in the classical case, our alternative multisolitons are found to obey elastic interactions of the N-KdV and M-cKdV solitons. To show this, we inductively construct tables to describe in detail the mechanism of the different wave interactions and the coefficients involved in them. As a particular scenario, it is found that each of the 1-cKdV and 1-KdV-1cKdV interaction cases may produce two independent criteria for the appearance of one-soliton solutions consisting of two humps in shape. A proper combination of these two conditions gives place to multi-hump solitons. We explicitly show the two-one, two-two, three-one and three-two humps for the two-component wave solutions. |
| first_indexed | 2024-12-19T10:44:54Z |
| format | Article |
| id | doaj.art-773b31fc1c324d14beb2b70ab6604424 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-12-19T10:44:54Z |
| publishDate | 2021-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-773b31fc1c324d14beb2b70ab66044242022-12-21T20:25:19ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812021-06-013100020Alternative solitons in the Hirota–Satsuma system via the direct methodHugo Parra Prado0Luis A. Cisneros-Ake1Posgrado en Ciencias Fisicomatemáticas, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 Cd. de México, Mexico; Corresponding author.Departamento de Matemáticas, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 Cd. de México, MexicoMultisolitons and multi-hump solitons are constructed for the coupled Korteweg–de Vries (cKdV) system introduced by Hirota and Satsuma (1981) in the context of the propagation of two waves interacting with different dispersion relations. The direct method analytically exhibit a new class of complementary or alternative soliton solutions functionally different to the traditional or classical multisolitons known (Hirota and Satsuma, 1981; Ramani et al., 1983; Parra Prado and Cisneros-Ake, 2020). As in the classical case, our alternative multisolitons are found to obey elastic interactions of the N-KdV and M-cKdV solitons. To show this, we inductively construct tables to describe in detail the mechanism of the different wave interactions and the coefficients involved in them. As a particular scenario, it is found that each of the 1-cKdV and 1-KdV-1cKdV interaction cases may produce two independent criteria for the appearance of one-soliton solutions consisting of two humps in shape. A proper combination of these two conditions gives place to multi-hump solitons. We explicitly show the two-one, two-two, three-one and three-two humps for the two-component wave solutions.http://www.sciencedirect.com/science/article/pii/S2666818120300206cKdV systemDirect methodAlternative multisolitonsMulti-hump solitons |
| spellingShingle | Hugo Parra Prado Luis A. Cisneros-Ake Alternative solitons in the Hirota–Satsuma system via the direct method Partial Differential Equations in Applied Mathematics cKdV system Direct method Alternative multisolitons Multi-hump solitons |
| title | Alternative solitons in the Hirota–Satsuma system via the direct method |
| title_full | Alternative solitons in the Hirota–Satsuma system via the direct method |
| title_fullStr | Alternative solitons in the Hirota–Satsuma system via the direct method |
| title_full_unstemmed | Alternative solitons in the Hirota–Satsuma system via the direct method |
| title_short | Alternative solitons in the Hirota–Satsuma system via the direct method |
| title_sort | alternative solitons in the hirota satsuma system via the direct method |
| topic | cKdV system Direct method Alternative multisolitons Multi-hump solitons |
| url | http://www.sciencedirect.com/science/article/pii/S2666818120300206 |
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