https://doi.org/10.1140/epjs/s11734-025-01853-z
Regular Article
Bäcklund transformations and nonlinear wave solutions for an extended (2+1)-dimensional Kadomtsev–Petviashvili equation
1
College of Mathematics Science and Center for Applied Mathematical Science, Inner Mongolia Normal University, 010022, Hohhot, China
2
School of Computer Information Management, Inner Mongolia University of Finance and Economics, 010070, Hohhot, China
a
zxh102089@163.com
b
zhongzhou-lan@buaa.edu.cn
Received:
2
June
2025
Accepted:
8
August
2025
Published online:
19
August
2025
This study investigates the analytical solutions and transformation properties for an extended (2+1)-dimensional Kadomtsev–Petviashvili equation with physical coefficients 
, 
, 
, 
. We establish bilinear and Bell-polynomial-typed Bäcklund transformations to derive multi-soliton solutions and characterize their propagation dynamics, including amplitude-dependent velocities and elastic interactions. Through the extended homoclinic test approach, breather wave solutions are derived, with rogue waves identified as their limiting case under infinite-period conditions. Additionally, one-periodic wave solution is constructed using the Hirota–Riemann method, and their connection to soliton solutions is rigorously demonstrated in the long-wave limit via symbolic computation. These results collectively enhance understanding of nonlinear wave phenomena governed by this system.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
