In this work, we investigate the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko (gBK) equation. Based on its bilinear form, the [Formula: see text]th-order breather solutions of the gBK equation are successful given by taking appropriate parameters. Furthermore, the [Formula: see text]th-order lump solutions of the gBK equation are obtained via the long-wave limit method. In addition, the semi-rational solutions are generated to reveal the interaction between lump solutions, soliton solutions, and breather solutions.

中文翻译：

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(2+1) 维广义 Bogoyavlensky–Konopelchenko 方程的一般高阶呼吸器、块和半有理解

在这项工作中，我们研究了 (2+1) 维广义 Bogoyavlensky-Konopelchenko (gBK) 方程。基于其双线性形式，gBK 方程的[公式：见正文]阶呼吸解是通过采用适当的参数而成功给出的。此外，通过长波极限法得到gBK方程的[公式：见正文]一次集中解。此外，生成半有理解以揭示团解、孤子解和呼吸解之间的相互作用。