Kopçasız Bahadır, Sağlam Fatma Nur Kaya, Bulut Hasan, Radwan Taha
Department of Computer Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, Istanbul, Türkiye.
Department of Mathematics, Faculty of Arts and Science, Tekirdağ Namık Kemal University, Tekirdağ, Türkiye.
Sci Rep. 2025 Apr 25;15(1):14542. doi: 10.1038/s41598-025-99080-y.
In this paper, we deal with the (n+1)-dimensional generalized Kadomtsev-Petviashvili equation (dgKPE). This is an important model in nonlinear science, with applications in various fields. Its integrability and rich soliton dynamics continue to attract researchers interested in the field of nonlinear partial differential equations (NLPDEs). We are interested in the new auxiliary equation method (NAEM). We reduce the equation to an ordinary differential equation (ODE) with the help of an appropriate wave transformation and search for different types of soliton solutions. Additionally, we demonstrated the efficacy of the NAEM as a straightforward yet powerful mathematical instrument for handling challenging issues, highlighting its potential to resolve the challenging problems related to the study of nonlinear equations. This technique yields several types of solutions for (n+1)-dgKPE, including trigonometric, hyperbolic, shock wave, singular soliton, exponential, and rational functions. A range of graphs showcasing the results are reviewed, as well as the wave behavior for the solutions in different circumstances. The obtained data provide important information for studying hydrodynamic waves, plasma fluctuations, and optical solitons. They also aid in understanding the behavior of the KPE in different physical situations. We clarify in this article how the (n+1)-dgKPE, when combined with NAEM, can result in better data transmission rates, optimized optical systems, and the advancement of nonlinear optics toward more dependable and efficient communication technologies. The obtained information clarifies the equation and opens up new avenues for investigation. To our knowledge, for this equation, these methods of investigation have not been utilized before. The accuracy of each solution has been verified using the Maple software program.
在本文中，我们研究(n + 1)维广义Kadomtsev - Petviashvili方程（dgKPE）。这是非线性科学中的一个重要模型，在各个领域都有应用。其可积性和丰富的孤子动力学一直吸引着非线性偏微分方程（NLPDEs）领域的研究人员。我们对新辅助方程法（NAEM）感兴趣。我们借助适当的波变换将该方程简化为常微分方程（ODE），并寻找不同类型的孤子解。此外，我们证明了NAEM作为一种直接而强大的数学工具在处理具有挑战性问题方面的有效性，突出了其解决与非线性方程研究相关的具有挑战性问题的潜力。该技术为(n + 1)-dgKPE产生了几种类型的解，包括三角函数、双曲函数、冲击波、奇异孤子、指数函数和有理函数。回顾了一系列展示结果的图形，以及不同情况下解的波动行为。所获得的数据为研究流体动力学波、等离子体波动和光学孤子提供了重要信息。它们也有助于理解KPE在不同物理情况下的行为。我们在本文中阐明了(n + 1)-dgKPE与NAEM结合时如何能够实现更好的数据传输速率、优化光学系统，并推动非线性光学朝着更可靠和高效的通信技术发展。所获得的信息阐明了该方程，并开辟了新的研究途径。据我们所知，对于这个方程，以前尚未使用过这些研究方法。每个解的准确性已使用Maple软件程序进行了验证。
