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<p>This paper studies the bilinear Bäcklund transformation, <i>N</i>-solitons and their derived multi-wave interaction solutions for an extended Kadomtsev-Petviashvili equation in (2+1)-dimensions. The Hirota bilinear form is given via Bell polynomial of bilinear equations, which is further used to obtain an auto-Bäcklund transformation and <i>N</i>-soliton solutions. Based on the new Bäcklund system provided, a lump-type wave solution is derived. By applying the Hirota condition analyses, we not only present the <i>N</i>-soliton solutions, but also present the multi-lump waves, multi-breather waves, and three types of hybrid-type interactions among lumps, breathers and kink solitons. The dynamic images further reveal that the multi-wave solutions derived from solitons possess essentially elastic characteristics, which well reflect the interaction phenomena of shallow-water waves. The mathematical model and findings of this study have potential application value in the fields of mathematical physics and fluid physics. The outcomes of this study are expected to play a significant role in numerous scientific fields.</p>

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Bäcklund transformation, N-solitons and standardized analyses of novel waves for a (2+1)-dimensional extended Kadomtsev-Petviashvili equation

  • 期刊论文

  • 发表日期：

    2026年4月24日

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  • Litao Gai,
  • Yujie Chen,
  • Wenyu Wu

摘要

This paper studies the bilinear Bäcklund transformation, N-solitons and their derived multi-wave interaction solutions for an extended Kadomtsev-Petviashvili equation in (2+1)-dimensions. The Hirota bilinear form is given via Bell polynomial of bilinear equations, which is further used to obtain an auto-Bäcklund transformation and N-soliton solutions. Based on the new Bäcklund system provided, a lump-type wave solution is derived. By applying the Hirota condition analyses, we not only present the N-soliton solutions, but also present the multi-lump waves, multi-breather waves, and three types of hybrid-type interactions among lumps, breathers and kink solitons. The dynamic images further reveal that the multi-wave solutions derived from solitons possess essentially elastic characteristics, which well reflect the interaction phenomena of shallow-water waves. The mathematical model and findings of this study have potential application value in the fields of mathematical physics and fluid physics. The outcomes of this study are expected to play a significant role in numerous scientific fields.