https://doi.org/10.1140/epjp/s13360-025-06321-0
Regular Article
Resonant soliton interactions of a generalized (2+1)-dimensional soliton equation via asymptotic analysis
1
School of Mathematics, North University of China, 030051, Taiyuan, Shanxi, People’s Republic of China
2
Department of Mathematics, Saint Xavier University, 60655, Chicago, IL, USA
a zhaozlhit@163.com, zhaozl@nuc.edu.cn
Received:
30
September
2024
Accepted:
14
April
2025
Published online:
21
May
2025
In this paper, we investigate the resonant soliton interactions of a generalized (2+1)-dimensional soliton equation. Via asymptotic analysis, we analyze the amplitudes and phase shifts after the interaction of two-soliton and obtain the expressions of two kinds of temporary intermediate solitons under different conditions. The resonant solutions of two- and three-soliton are discussed, and the exact expressions of new resonant soliton branches are obtained. In particular, by controlling the amplitude of the temporary intermediate soliton generated by the interaction of two-soliton to zero, a new “curved soliton” of the bound state is generated, and by controlling the amplitude of the new resonant branch generated by the interaction of resonant three-soliton to zero, a resonant X-type soliton and a resonant Y-type soliton are obtained, which are works that have not been discussed before. The 2D and 3D images are used to describe these resonant interactions. This study lays a foundation for us to study the resonant interaction between solitons and other nonlinear waves.
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 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.
