In this paper, based on the Hirota bilinear method, the high-order breathers and interaction solutions between solitons and breathers of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation are investigated. The lump and semi-rational solutions are obtained by applying the long wave limit of the N-soliton solution. Two types of semi-rational solutions are derived by choosing specific parameters, which are the mixture of the lump solution and solitons, and the mixture of the lump solution and breathers. Furthermore, the time evolution diagram illustrate the dynamic behavior of these solutions.

中文翻译：

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(2+1) 维 Yu-Toda-Sasa-Fukuyama 方程的高阶呼吸和半有理解

本文基于 Hirota 双线性方法，研究了 (2+1) 维 Yu-Toda-Sasa-Fukuyama 方程的高阶呼吸子和孤子与呼吸子之间的相互作用解。块解和半有理解是通过应用ñ-孤子溶液。通过选择特定的参数，导出了两种半有理解，即块解和孤子的混合，以及块解和呼吸器的混合。此外，时间演化图说明了这些解决方案的动态行为。