Study on the (2+1)-dimensional extension of Hietarinta equation: soliton solutions and Bäcklund transformation

The (1+1)-dimensional bilinear Hietarinta equation was firstly proposed when searching for integrable nonlinear evolution equations by the three-soliton method. In this paper, we focus on the (2+1)-dimensional extension of Hietarinta equation, which enjoys potential application in environmental engi...

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Bibliographic Details
Published in:Physica scripta 2023-09, Vol.98 (9), p.95225
Main Authors: Gao, Di, Lü, Xing, Peng, Ming-Shu
Format: Article
Language:English
Subjects:
Bell polynomial
Bäcklund transformation
Hietarinta bilinear equation
soliton solution
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Summary:The (1+1)-dimensional bilinear Hietarinta equation was firstly proposed when searching for integrable nonlinear evolution equations by the three-soliton method. In this paper, we focus on the (2+1)-dimensional extension of Hietarinta equation, which enjoys potential application in environmental engineering. Based on the bilinear form, one-soliotn and two-soliton solutions are derived. Bilinear Bäcklund transformation and Bell-polynomial-typed Bäcklund transformation are derived through the Hirota bilinear method and Bell polynomials, respectively. The three-dimensional plots of soliton solutions have been given by selecting appropriate parameters.
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/ace8d0