https://doi.org/10.1140/epjp/s13360-022-02710-x
Regular Article
Bäcklund transformations for the modified short pulse equation and complex modified short pulse equation
1
Department of Mathematics, China University of Mining and Technology, 100083, Beijing, People’s Republic of China
2
School of Mathematics and Statistics, Nanning Normal University, 530001, Nanning, Guangxi, People’s Republic of China
Received:
1
December
2021
Accepted:
9
April
2022
Published online:
22
April
2022
It is demonstrated that under a reciprocal transformation, the modified short pulse (mSP) equation is brought to the associated mSP equation, which is shown to be equivalent to the associated SP equation. This connection allows us to build a Bäcklund transformation (BT) and the general formula of its iterations for the mSP equation. In addition to the (real) mSP equation, we further apply the BT method to the complex modified short pulse (cmSP) equation, and both its BT and nonlinear superposition formula are worked out. As applications, for the cmSP equation we calculate its various solutions, such as the soliton solutions, cuspon solutions, breather solutions and their interaction solutions.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
