In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.

在这项研究中，我们研究了一个新的四阶可积非线性方程。首先，通过有效的Hirota双线性方法，我们建立了新颖的解决方案类型，包括通气，流氓和三波解决方案。其次，借助李对称性，我们报告了所研究方程的不变性，如变换组，换向器和伴随表示表。通过非线性自伴（NSA）找到差分替换，然后建立相关的守恒律。我们通过3维和轮廓图展示了所获得解决方案的一些动力学特征。