https://doi.org/10.1140/epjp/s13360-020-00469-7
Regular Article
Multiple breathers and high-order rational solutions of the new generalized (3+1)-dimensional Kadomtsev–Petviashvili equation
School of Mathematics, China University of Mining and Technology, 221116, Xuzhou, Jiangsu, China
Received:
3
April
2020
Accepted:
15
May
2020
Published online: 8 June 2020
In this paper, we consider a new generalized KP equation which is obtained by adding the extra term utz in the previous equation. Based on these detailed discussions in the previous reference documentations, we know that solitons, breathers, lump waves, and rogue waves are four typical local waves. Therefore, we mainly focus on investigating the multi-soliton solutions, high-order breather solutions, and high-order rational solutions. The high-order breather solutions can be derived by taking complex conjugate parameters in the multi-soliton solutions. Applying the long wave limit method to the multi-soliton solutions, we conclude Theorem 3.1 which can be used directly to obtain high-order rational solutions. Meanwhile, for the case of three-soliton and five-soliton, the elastic interaction solutions among two parallel breathers and one soliton as well as between one breather and one soliton also can be derived, respectively. For all these types of exact solutions, we provide corresponding graphics to illustrate their dynamical characteristics in the end.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
