In this work, the abundant exact closed-form solutions and dynamics of solitons for the double-chain deoxyribonucleic acid (DNA) model is obtained by utilizing the generalized exponential rational function (GERF) method. Deoxyribonucleic acid (DNA) retains the genetic information that creatures need to live and reproduce themselves. We obtained several novel exact soliton and exponential rational functional solutions in the shapes of dynamics of solitons like multi-solitons, breather-type solitons, abundant elastic interactions between multi-solitons, and nonlinear waves, oscillating multi-solitons, and Lump solitons. These derived solutions were never reported in the literature. The dynamical structures of some exact solitons are exhibited graphically by assigning suitable values to the free parameters via 3D figures. The generated solutions can be more useful and help to explain the internal interactions of the double-chain DNA model. The symbolic computational work and the obtained solutions show that the present proposed GERF method is effective, robust, and straightforward. Moreover, these types of higher-order NLEEs can be solved using the current technique.

在这项工作中，利用广义指数有理函数（GERF）方法获得了双链脱氧核糖核酸（DNA）模型的丰富的精确封闭形式的孤子解和动力学。脱氧核糖核酸 (DNA) 保留了生物生存和繁殖所需的遗传信息。我们在多孤子、呼吸型孤子、多孤子之间丰富的弹性相互作用、非线性波、振荡多孤子和块孤子等孤子动力学形状方面获得了几种新颖的精确孤子和指数有理泛函解。这些衍生的解决方案从未在文献中报道过。通过 3D 图形为自由参数分配合适的值，以图形方式展示了一些精确孤子的动力学结构。生成的解决方案可能更有用，有助于解释双链 DNA 模型的内部相互作用。符号计算工作和获得的解决方案表明，目前提出的 GERF 方法是有效、稳健和直接的。此外，可以使用当前技术解决这些类型的高阶 NLEE。