In this paper, we present a model that is of the utmost importance in the field of waves and the propagation of pulses. This model was chosen with great care, because it is somewhat complicated in the calculations, and also because finding solutions to it represents a breakthrough in this field. The process of finding solutions does not mean finding solutions just because they are solutions, but the goal is to find solutions when generating one after the other and interactions occur between them, each wave must keep form. The topic is very important and exciting for all researchers to do their best. In the end, we would like to say that the accuracy of solutions depends mainly on the accuracy of the method used. All previous researchers did not provide the shapes that explain their solutions, and therefore in this work, we will provide what we have come up with in full transparency. At the end of the work, we introduce the explanations for all the results that we obtained.

在本文中，我们提出了一个在波和脉冲传播领域中至关重要的模型。选择该模型非常谨慎，因为它的计算有些复杂，并且因为找到解决方案的方法代表了该领域的突破。寻找解决方案的过程并不意味着仅仅因为它们是解决方案而寻找解决方案，而是目标是要在一个接一个地生成一个解决方案并且解决方案之间发生相互作用时找到解决方案，每一波都必须保持形式。对于所有研究人员来说，这个话题都是非常重要和令人兴奋的。最后，我们要说的是，解决方案的准确性主要取决于所使用方法的准确性。以前所有的研究人员都没有提供解释其解决方案的形状，因此在这项工作中，我们将以完全透明的方式提供我们提出的建议。在工作的最后，我们介绍了所获得的所有结果。