In this paper, a variety of novel exact traveling wave solutions are constructed for the \((2+1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation via analytical techniques, namely, extended rational sine-cosine method and extended rational sinh-cosh method. The physical meaning of the geometrical structures for some of these solutions is discussed. Obtained solutions are expressed in terms of singular periodic wave, solitary waves, bright solitons, dark solitons, periodic wave and kink wave solutions with specific values of parameters. For the observation of physical activities of the problem, achieved exact solutions are vital. Moreover, to find analytical solutions of the proposed equation many methods have been used but given methodologies are effective, reliable and gave more and novel exact solutions.

在本文中，通过解析技术，即扩展有理正余弦方法和扩展有理数方法，为\((2+1)\)维 Boiti-Leon-Manna-Pempinelli 方程构建了多种新的精确行波解。sinh-cosh 方法。讨论了其中一些解的几何结构的物理意义。得到的解以具有特定参数值的奇异周期波、孤波、亮孤子、暗孤子、周期波和扭结波解表示。对于观察物理活动的问题，获得精确的解是至关重要的。此外，为了找到所提出方程的解析解，已经使用了许多方法，但给定的方法是有效的、可靠的，并给出了更多和新颖的精确解。