In this paper, we analyze kink-like analytical solutions in a real scalar theory with an arcsin dynamics inspired by the arcsin electrodynamics presented in Kruglov (2015). This analysis is done by means of the first-order formalism. This formalism provides a framework where the equations of motion can be simplified by preserving the linear stability of the theory. In this work, the deformation procedure is implemented with the aim of finding exact solutions in systems with generalized dynamics. Along with the paper, we explore how the first-order formalism is implemented in the arcsin kinetics and how such a term influences the kink-like solutions. As a part of the result of our paper, we show that the kink-like solutions are similar to the ones obtained in the standard scalar kinetic theory. We also show that the extra parameter, that controls the non-linearities of the model, plays an essential role in the energy densities and stability potentials. These quantities vary according to this parameter. The goals here are to show how the first-order framework is implemented in this arcsin scenario and to present the analytical kink-like solutions that can be found by means of the first-order framework and deformation method.

中文翻译：

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反正弦实标量动力学中的扭结结构

在本文中，我们使用受 Kruglov (2015) 中提出的反正弦电动力学启发的反正弦动力学分析了真实标量理论中的类扭结解析解。这种分析是通过一阶形式主义来完成的。这种形式主义提供了一个框架，可以通过保持理论的线性稳定性来简化运动方程。在这项工作中，变形程序的实施目的是在具有广义动力学的系统中找到精确解。与论文一起，我们探讨了如何在反正弦动力学中实现一阶形式主义，以及这样的术语如何影响类扭结的解决方案。作为我们论文结果的一部分，我们表明类扭结解与标准标量动力学理论中获得的解相似。我们还表明，额外的参数，控制模型的非线性，在能量密度和稳定势中起着至关重要的作用。这些数量根据此参数而变化。这里的目标是展示一阶框架是如何在这个 arcsin 场景中实现的，并展示可以通过一阶框架和变形方法找到的分析类扭结解。