This article explores the abundant solitary wave solutions of the conformable coupled Jaulent–Miodek (JM) equations appearing in applied physics. The aforesaid coupled equations belong to the family of shallow-water wave equations. Two recent modified integration schemes are used for the first time to produce a novel solitary wave, trigonometric and other solutions with some free parameters in the conformable derivative sense. In particular, the modified Kudryashov and [Formula: see text]-expansion schemes are used to illustrate the wave propagations through aforesaid solutions of the JM equations. Furthermore, a comparison is made with some recent results and the dynamics of the obtained solutions are displayed for the reader via soft computation. The outcomes reveal that the methods are effective and provide a direct way of finding novel solutions.

中文翻译：

---

应用物理学中出现的分数耦合 Jaulent-Miodek 方程的丰富孤立波解

本文探讨了应用物理学中出现的适形耦合 Jaulent-Miodek (JM) 方程的丰富孤立波解。上述耦合方程属于浅水波动方程族。两个最近修改的积分方案首次用于产生一种新颖的孤立波、三角函数和其他具有一些自由参数的解。特别地，修改的 Kudryashov 和 [公式：见正文]-展开方案用于说明波通过上述 JM 方程解的传播。此外，还与一些最近的结果进行了比较，并通过软计算向读者展示了所获得解决方案的动态。