Abstract
On the bases of N-soliton solutions of Hirota’s bilinear method, anomalously interacting lump patterns of (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation can be generated through normally interacting lump chains by two different paths. In the first path, through tending the periods of M normally lump chains with close velocities to infinity, \(M(M+1)/2\) anomalously interacting lumps are obtained directly. In the second path, there are two steps to generate lump waves. Firstly, M normally interacting lump chains degenerate into M anomalously interacting lump chains with the same parameters as the first path. Secondly, the anomalously lump waves can be derived from the M anomalously interacting lump chains when the period tends to infinity. Moreover, the distance between anomalously interacting lump chains varies with time proportional to \(\ln {|t|}\).
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Funding
This work is supported by National Natural Science Foundation of China under Grant Nos. 12175111, 12275144, 12235007 and 11975131 and K.C.Wong Magna Fund in Ningbo University.
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Appendices
Appendix A
Functions \(h_j\) and \(h_{jk}\) \((j,k=1,2,3)\) in Eq. (26) are determined as follows:
In addition, \(h_{21}=h_{12}^*\), \(h_{31}=h_{13}^*\) and \(h_{32}=h_{23}^*\).
Appendix B
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Sun, Y., Li, B. Creation of anomalously interacting lumps by degeneration of lump chains in the BKP equation. Nonlinear Dyn 111, 19297–19313 (2023). https://doi.org/10.1007/s11071-023-08857-1
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DOI: https://doi.org/10.1007/s11071-023-08857-1