This paper addresses the soliton solutions of the Mel’nikov system by the complex amplitude ansatz method and the He’s variational principle. The bright, anti-bright, dark, anti-dark, kink, anti-kink, bell-shaped, breather and homoclinic orbits are obtained as different possible solutions of the Mel’nikov system by the two methods. The solutions and their dynamical behaviour captured by the two methods are discussed. The solutions contain enough number of free physical parameters. These solutions give a better explanation of the associated physical phenomena. The modulation instability analysis of the steady-state solutions of the Mel’nikov system is investigated. This investigation has revealed that the Mel’nikov system is stable against small perturbation for a certain range of perturbation wave numbers. Apart from this, these solutions also help in validating the amount of accuracy in the numerical solutions and to perform the stability analysis further.

本文通过复振幅ansatz方法和He's变分原理解决了Mel'nikov系统的孤子解。通过两种方法获得了明亮的，反明亮的，黑暗的，反黑暗的，扭结的，反扭结的，钟形的，通气的和同斜的轨道，作为梅尔尼科夫系统的不同可能解。讨论了通过两种方法捕获的解及其动力学行为。这些解决方案包含足够数量的免费物理参数。这些解决方案可以更好地解释相关的物理现象。研究了梅尔尼科夫系统稳态解的调制不稳定性分析。这项研究表明，梅尔尼科夫系统在一定范围的摄动波数范围内对小扰动是稳定的。除此之外，