Affiliations:
1School of Mathematics and Statistics, Weifang University, Weifang 261061, China
2Jingu College, Tianjin Normal University, Tianjin 300387, China
The study of Bäcklund transformations and solutions for (3+1)-dimensional nonlinear evolution equations is important in integrability research, as there are only a few existing studies on this topic. In this paper, we present a Bäcklund transformation (BT) for a newly generalized (3+1)-dimensional Kadomtsev–Petviashvili (3dKP) equation by introducing new Hamiltonian vector fields. Using the derived BT and a given formal solution, we obtain several new soliton solutions. Finally, we propose a new superposition formula, based on the BT, that combines different solutions.
Bäcklund transformation, Soliton solutions, Hamiltonian vector fields, Kadomtsev–Petviashvili equation, Superposition formula
https://doi.org/10.21833/ijaas.2025.09.021
Sun, Y., Liu, W., & Liu, M. (2025). A Bäcklund transformation and superposition formula for a new high-dimensional nonlinear equation. International Journal of Advanced and Applied Sciences, 12(9), 215–219. https://doi.org/10.21833/ijaas.2025.09.021