论文标题
（4 + 1） - 维fokas方程的减少及其解决方案
Reductions of the (4 + 1)-dimensional Fokas equation and their solutions
论文作者
论文摘要
在本文中研究了Kadomtsev-PetviaShvili（KP）和Davey-Stewartson方程的可集成扩展。我们将将这一可集成的扩展称为（4+1） - 维fokas方程。基于Hirota的双线性方法和KP层次结构减少方法构建了（4 + 1） - 维fokas方程（4 + 1）二维fokas方程的孤子，呼吸，有理和半理性解的决定因素表达式。这些新精确溶液的复杂动力学在三维图和二维轮廓图中显示。有趣的是，通过选择模型的自由参数的不同值，获得的高阶肿块的模式与（1 + 1）维度中的流氓波的模式相似。此外，提出了三种新的半理性解，还讨论了肿块裂变和融合过程的分类。此外，我们通过减少（4 + 1）维fokas方程的解决方案来获得（3 + 1）维克方程（3 + 1）维克方程的有理和半理性解决方案的新方法。所有这些结果表明，（4 + 1）维fokas方程是KP和DS方程的有意义的多维扩展。获得的结果可能在流体动力学，非线性光学和光子学，等离子体中的离子声波，Bose-Einstein冷凝物中的物质波以及铁磁培养基中的声波中可能有用。
An integrable extension of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations is investigated in this paper.We will refer to this integrable extension as the (4+1)-dimensional Fokas equation. The determinant expressions of soliton, breather, rational, and semi-rational solutions of the (4 + 1)-dimensional Fokas equation are constructed based on the Hirota's bilinear method and the KP hierarchy reduction method. The complex dynamics of these new exact solutions are shown in both three-dimensional plots and two-dimensional contour plots. Interestingly, the patterns of obtained high-order lumps are similar to those of rogue waves in the (1 + 1)-dimensions by choosing different values of the free parameters of the model. Furthermore, three kinds of new semi-rational solutions are presented and the classification of lump fission and fusion processes is also discussed. Additionally, we give a new way to obtain rational and semi-rational solutions of (3 + 1)-dimensional KP equation by reducing the solutions of the (4 + 1)-dimensional Fokas equation. All these results show that the (4 + 1)-dimensional Fokas equation is a meaningful multidimensional extension of the KP and DS equations. The obtained results might be useful in diverse fields such as hydrodynamics, non-linear optics and photonics, ion-acoustic waves in plasmas, matter waves in Bose-Einstein condensates, and sound waves in ferromagnetic media.
