https://doi.org/10.1140/epjp/s13360-023-04682-y
Regular Article
Soliton molecules, multi-breathers and dynamical behaviors of the Lakshmanan–Porsezian–Daniel equation
Department of Mathematics, Zhejiang University of Technology, 310014, Hangzhou, China
Received:
21
April
2023
Accepted:
10
November
2023
Published online:
28
November
2023
In this work, we investigate the Lakshmanan–Porsezian–Daniel (LPD) equation with high-order nonlinear and dispersion terms which can describe an inhomogeneous one-dimensional anisotropic Heisenberg ferromagnetic spin chain and alpha helical protein. With the aid of auxiliary function, the bilinear form of the LPD equation is constructed. Multi-soliton solutions are obtained by solving the corresponding bilinear form. Multi-breather solutions are presented by assuming the complex conjugation relations on the parameters of the multi-solitons. The dynamics of one breather, two breathers and their interactions are constructed by selecting the appropriate parameters. The strength of the high-order nonlinear and dispersion effects plays a key role in the breather solutions. Soliton molecule, the breather–soliton molecule and the breather molecule are discovered by applying the velocity resonance conditions. The interactions among the soliton molecules, which could be observed in marine and oceanic waters, are investigated through numerical simulation.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
