This paper presents an improved Cham method as an efficient technique for obtaining analytical exact solutions to nonlinear partial differential equations. We apply this method to solve the nonlinear Schrödinger equation in conformable operator, a challenging equation frequently used in various scientific fields. The method enables us to derive different traveling wave solutions, such as kink, coindal waves, breather waves, periodic singular solutions, and periodic multi-wave solitons. We also provide graphical representations of some of the obtained solutions to help understand their dynamic characteristics. These results highlight the effectiveness and adaptability of the method and demonstrate its potential to solve other partial differential equations.

本文提出了一种改进的 Cham 方法，作为获得非线性偏微分方程解析精确解的有效技术。我们应用这种方法来求解一致算子中的非线性薛定谔方程，这是一个在各个科学领域中经​​常使用的具有挑战性的方程。该方法使我们能够导出不同的行波解，例如扭结波、硬币波、呼吸波、周期性奇异解和周期性多波孤子。我们还提供了一些获得的解决方案的图形表示，以帮助了解它们的动态特性。这些结果突出了该方法的有效性和适应性，并展示了其求解其他偏微分方程的潜力。