In the current article, we will apply the scaling invariance technique to find conservation laws (CLs) for the nonlinear Chiral Schrödinger equation (NLCSE) with variable coefficients and the $(2+1)$-dimensional Maccari system. In addition to the establishment of CLs for these models, we will also look for diverse forms of dromions (solitons) solutions in polynomial forms such as optical solitary and soliton wave with Jacobi elliptic solutions. These solutions will be obtained by applying a well known and renowned integration scheme known as the unified scheme (US). Moreover, the solvability of these governing models is investigated by means of a much blooming algorithm, which is known as the Painlevé algorithm.

在当前的文章中，我们将应用定标不变性技术来找到具有可变系数的非线性手性Schrödinger方程（NLCSE）的守恒律（CLs）。 $（\mathrm{2个}+\mathrm{1个}）$维Maccari系统。除了为这些模型建立CL之外，我们还将寻找多项式形式的dromion（孤子）解决方案，例如光学孤子和孤子波以及Jacobi椭圆解。这些解决方案将通过应用众所周知的，称为统一方案（US）的集成方案来获得。此外，这些控制模型的可解性是通过大量开花算法（称为Painlevé算法）进行研究的。