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<p>In the study of nonlinear evolution equations, the three-soliton method was implemented to investigate the integrability of the (1+1)-dimensional bilinear Hietarinta equation. In this paper, we study a (2+1)-dimensional version of the Hietarinta equation. It will be shown that the transformed (2+1)-dimensional Hietarinta equation admits a trivial balancing number. The symmetry method will be used to derive exact solutions of this equation. It will be further shown that although the balancing number is trivial, this equation admits some special analytical solutions via ansatz methods. Furthermore, we derive low-order conservation of the aforesaid equation. Finally, a brief physical interpretation of the derived results is presented.</p>

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A Novel Study of the (2+1)-Dimensional Hietarinta Equation with a Trivial Balancing Number

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月3日

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  • M. F. Seele,
  • B. Muatjetjeja,
  • T. G. Motsumi,
  • A. R. Adem

摘要

In the study of nonlinear evolution equations, the three-soliton method was implemented to investigate the integrability of the (1+1)-dimensional bilinear Hietarinta equation. In this paper, we study a (2+1)-dimensional version of the Hietarinta equation. It will be shown that the transformed (2+1)-dimensional Hietarinta equation admits a trivial balancing number. The symmetry method will be used to derive exact solutions of this equation. It will be further shown that although the balancing number is trivial, this equation admits some special analytical solutions via ansatz methods. Furthermore, we derive low-order conservation of the aforesaid equation. Finally, a brief physical interpretation of the derived results is presented.