International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12

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 Volume 12, Issue 9 (September 2025), Pages: 215-219

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 Original Research Paper

A Bäcklund transformation and superposition formula for a new high-dimensional nonlinear equation

 Author(s): 

 Yanmei Sun 1, *, Wei Liu 2, Ming Liu 2

 Affiliation(s):

  1School of Mathematics and Statistics, Weifang University, Weifang 261061, China
  2Jingu College, Tianjin Normal University, Tianjin 300387, China

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 * Corresponding Author. 

   Corresponding author's ORCID profile:  https://orcid.org/0000-0002-1339-4999

 Digital Object Identifier (DOI)

  https://doi.org/10.21833/ijaas.2025.09.021

 Abstract

The study of Bäcklund transformations and solutions for (3+1)-dimensional nonlinear evolution equations is important in integrability research, as there are only a few existing studies on this topic. In this paper, we present a Bäcklund transformation (BT) for a newly generalized (3+1)-dimensional Kadomtsev–Petviashvili (3dKP) equation by introducing new Hamiltonian vector fields. Using the derived BT and a given formal solution, we obtain several new soliton solutions. Finally, we propose a new superposition formula, based on the BT, that combines different solutions.

 © 2025 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Bäcklund transformation, Soliton solutions, Hamiltonian vector fields, Kadomtsev–Petviashvili equation, Superposition formula

 Article history

 Received 5 April 2025, Received in revised form 15 August 2025, Accepted 20 August 2025

 Acknowledgment

This work is supported by the National Natural Science Foundation of China (Grant No. 11971475). 

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Sun Y, Liu W, and Liu M (2025). A Bäcklund transformation and superposition formula for a new high-dimensional nonlinear equation. International Journal of Advanced and Applied Sciences, 12(9): 215-219

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