https://doi.org/10.1140/epjp/s13360-022-02412-4
Regular Article
The generation mechanism of multiple-pole solutions for the fifth-order mKdV equation
1
Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, 510631, Guangzhou, People’s Republic of China
2
School of Mathematics and Statistics, Ningbo University, 315211, Ningbo, People’s Republic of China
3
Department of Mathematics, Saint Xavier University, 60655, Chicago, IL, USA
Received:
14
October
2021
Accepted:
23
January
2022
Published online:
2
February
2022
A skillful partial limit approach is proposed in this paper, which is used to generate some new solutions called multiple-pole solutions directly from the well-known N-soliton solution for the fifth-order modified Korteweg–de Vries equation. Based on the traditional limit method developed by us, the dark double-pole solution neglected by some scholars is found. Furthermore, we creatively give a general method for constructing triple-pole solutions, multiple-pole solutions and degeneration of breather solutions. Moreover, the dynamical properties of these multiple-pole solutions are discussed in detail.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
