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<p>This study investigates localized wave solutions for a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko-like (gBK-like) equation. Using the Hirota’s bilinear formalism, we extend the bilinear neural network framework to include one hidden layer for constructing test functions. With the aid of Maple software, we analyze lump-type, lump-periodic, lump-stripe, and kink-wave solutions of the (2+1)-dimensional gBK-like equation. In particular, we examine the conditions that ensure the analyticity, positivity, and localization of lump-type solutions. Furthermore, we demonstrate the evolutionary and dynamical properties of these solutions obtained through suitable real parameter choices. This analysis provides valuable insights into the dynamical behaviors of nonlinear evolution equations.</p>

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Properties of localized waves in a generalized (2+1)-dimensional Bogoyavlensky-Konopelchenko-like equation

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Chunyan Qin,
  • Dongxing Fu,
  • Runfa Zhang,
  • Yaohong Li,
  • Xiancai Gao

摘要

This study investigates localized wave solutions for a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko-like (gBK-like) equation. Using the Hirota’s bilinear formalism, we extend the bilinear neural network framework to include one hidden layer for constructing test functions. With the aid of Maple software, we analyze lump-type, lump-periodic, lump-stripe, and kink-wave solutions of the (2+1)-dimensional gBK-like equation. In particular, we examine the conditions that ensure the analyticity, positivity, and localization of lump-type solutions. Furthermore, we demonstrate the evolutionary and dynamical properties of these solutions obtained through suitable real parameter choices. This analysis provides valuable insights into the dynamical behaviors of nonlinear evolution equations.