二维立方五元复数金兹堡-朗道方程的解析解

IF 1.2 Q2 MATHEMATICS, APPLIED
F. W. Tchuimmo, J. B. G. Tafo, A. Chamgoue, N. C. T. Mezamo, F. Kenmogne, L. Nana
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引用次数: 0

摘要

在亚临界分岔附近,深入研究了一类二维系统中行波的动力学行为,该系统的振幅服从二维复立方-五次方金兹堡-朗道方程。然后,利用分岔法预测所考虑的波方程的解的性质。它被用于将二维复立方-五次方金兹堡-朗道方程简化为五次方非线性常微分方程,易于求解。在一些参数约束条件下,得到了平衡点并绘制了相位图。根据平衡点的性质,新常微分方程获得的这些相位肖像的特殊性在于同折线或异折线轨道的存在。对于某些参数,轨道从一个固定点开始,经过另一个固定点,然后返回同一固定点,这预示着存在一对脉冲-暗孤子的组合。对于其他参数,也有将三个平衡点连接起来的轨道,预示着一对暗孤子的存在。这些结果非常重要,可以预测许多领域的相同解,特别是波现象、机械系统或横向加热流体层。此外,根据参数系统的取值,还可以找到所预测解的解析表达式。我们还绘制了这些解的三维图以及它们在传播方向上的二维图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation
The dynamical behaviour of traveling waves in a class of two-dimensional system whose amplitude obeys the two-dimensional complex cubic-quintic Ginzburg-Landau equation is deeply studied as a function of parameters near a subcritical bifurcation. Then, the bifurcation method is used to predict the nature of solutions of the considered wave equation. It is applied to reduce the two-dimensional complex cubic-quintic Ginzburg-Landau equation to the quintic nonlinear ordinary differential equation, easily solvable. Under some constraints of parameters, equilibrium points are obtained and phase portraits have been plotted. The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. For some parameters, one has the orbits starting to one fixed point and passing through another fixed point before returning to the same fixed point, predicting then the existence of the combination of a pair of pulse-dark soliton. One has also for other parameters, the orbits linking three equilibrium points predicting the existence of a dark soliton pair. These results are very important and can predict the same solutions in many domains, particularly in wave phenomena, mechanical systems, or laterally heated fluid layers. Moreover, depending on the values of parameter systems, the analytical expression of the solutions predicted is found. The three-dimensional graphs of these solutions are plotted as well as their 2D plots in the propagation direction.
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来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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