https://doi.org/10.1140/epjp/s13360-025-06047-z
Regular Article
Generation of anomalously scattered lump waves for (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation
1
School of Mathematical Sciences, Beihang University, 100191, Beijing, China
2
School of Mathematics and Information Science, Zhongyuan University of Technology, 450007, Zhengzhou, China
Received:
6
December
2024
Accepted:
18
January
2025
Published online:
2
February
2025
The anomalous scattering of lump waves governed by the Date–Jimbo–Kashiwara–Miwa (DJKM) equation is explored via two distinct methods. The second-order anomalously scattered lump is derived by degenerating the M-lump solution under the limit of infinite phase. Higher order anomalously scattered lumps are obtained through the degeneration of lump chains described by infinite periods, with analyses of two types of degenerate lump chains. A thorough asymptotic analysis is employed to investigate both the dynamic behavior and scattering angles of the anomalous scattering phnomena. Notably, the triangular structures of higher order lumps are found to be closely related to the Yablonskii-Vorob’ev polynomials. These insights may deepen our understanding of the intrinsic characteristics of lump waves.
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© 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.
