TY - JOUR
T1 - Alternative solitons in the Hirota–Satsuma system via the direct method
AU - Parra Prado, Hugo
AU - Cisneros-Ake, Luis A.
N1 - Publisher Copyright:
© 2020 The Authors
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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.
KW - Alternative multisolitons
KW - Direct method
KW - Multi-hump solitons
KW - cKdV system
UR - http://www.scopus.com/inward/record.url?scp=85123889223&partnerID=8YFLogxK
U2 - 10.1016/j.padiff.2020.100020
DO - 10.1016/j.padiff.2020.100020
M3 - Artículo
AN - SCOPUS:85123889223
SN - 2666-8181
VL - 3
JO - Partial Differential Equations in Applied Mathematics
JF - Partial Differential Equations in Applied Mathematics
M1 - 100020
ER -