https://doi.org/10.1140/epjp/s13360-022-03238-w
Regular Article
Multiple-pole soliton, periodic and rational solutions of the fifth-order modified Korteweg–de Vries equation
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, 210044, Nanjing, People’s Republic of China
Received:
10
October
2021
Accepted:
25
August
2022
Published online:
5
September
2022
The multiple-pole soliton, periodic and rational solutions for the fifth-order modified Korteweg–de Vries equation are derived via the robust inverse scattering transform method. More specifically, the first-order spatial periodic solution and first-order, second-order rational solutions with a nonzero constant background are obtained explicitly. Furthermore, a second-order pole soliton formula is found by onefold application of Darboux transformation under the condition of zero background with associated spectral data consisting of a single pair of conjugate poles of order 2. The dynamical behaviors of these solutions are also depicted in detail.
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