In this work, we explore the dynamics of molecules in torsionally stressed DNA subjected to periodic external forces, specifically microwave radiation. Our approach involves constructing a novel continuum model based on a discrete model. Remarkably, this continuum model has not been analytically solved in existing literature, which motivates us to derive analytic solutions for investigating DNA s dynamical behavior. Our primary objective is to examine the impact of an external field (such as microwave radiation) on DNA dynamics, potentially affecting its structural integrity. Scientifically, we know that DNA molecules exposed to microwaves can suffer damage. Here, we focus on stability (or instability) to determine deterministic outcomes. Analytic solutions are essential for this purpose. The model equations governing torsional DNA (TDNA) behavior are non-autonomous and, in some cases, not integrable, meaning no exact solutions exist. Consequently, we rely on approximate solutions. Our chosen method is the extended unified method, allowing us to control errors through parameter selection. We consider two scenarios: when the torsional angle is smaller than one or completely free. Exact solutions emerge only when stacking and chain curvature constants are equal, otherwise, we derive approximate solutions. Numerical results: Numerical representations reveal that the localization of DNA molecules depends significantly on the microwave amplitude (MWA) and damping rate. Additionally, a critical MWA or DA value exists beyond which TDNA undergoes deformation. Stability analysis plays a crucial role in understanding these intricate dynamics. The present study sheds light on the interplay between external fields, DNA stability, and structural changes. Analytic solutions provide valuable insights into this complex system, with potential implications for biological processes and health.

在这项工作中，我们探索了受周期性外力（特别是微波辐射）作用的扭转应力 DNA 中分子的动力学。我们的方法涉及基于离散模型构建新颖的连续模型。值得注意的是，这种连续体模型在现有文献中尚未得到解析解决，这促使我们推导出解析解来研究 DNA 的动态行为。我们的主要目标是检查外部场（例如微波辐射）对 DNA 动力学的影响，从而可能影响其结构完整性。从科学角度来说，我们知道暴露于微波的 DNA 分子会受到损害。在这里，我们关注稳定性（或不稳定性）来确定确定性结果。为此，分析解决方案至关重要。控制扭转 DNA (TDNA) 行为的模型方程是非自治的，并且在某些情况下不可积，这意味着不存在精确解。因此，我们依赖近似解。我们选择的方法是扩展统一方法，允许我们通过参数选择来控制错误。我们考虑两种情况：扭转角小于 1 或完全自由时。只有当堆叠曲率常数和链曲率常数相等时，才会出现精确解，否则，我们会得出近似解。数值结果：数值表示表明 DNA 分子的定位很大程度上取决于微波振幅 (MWA) 和阻尼率。此外，还存在一个临界 MWA 或 DA 值，超过该值 TDNA 就会发生变形。稳定性分析在理解这些复杂的动态过程中起着至关重要的作用。本研究揭示了外部场、DNA 稳定性和结构变化之间的相互作用。分析解决方案为这一复杂系统提供了宝贵的见解，对生物过程和健康具有潜在影响。