开放式信息测量系统设计中的领域结构形成

IF 0.2 Q4 INSTRUMENTS & INSTRUMENTATION Devices and Methods of Measurements Pub Date : 2022-12-21 DOI:10.21122/2220-9506-2022-13-4-256-262
M. A. Knyazev
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引用次数: 0

摘要

开放系统在测量装置设计中具有越来越重要的意义和应用的可能性。现在一个本质上的非线性模型被用于这样的系统。对于这些目的,摄动方法是不够的。新型模型的解以孤子或扭结或类似物体的形式存在。Fisher-Kolmogorov-Petrovskii-Piskunov方程就是其中之一。该方程用于描述对流-反应-扩散过程。这种过程用于研究非平衡开放系统中的自组织和结构的形成。本文的目的是为考虑空间非齐次性的修正方程Fisher-Kolmogorov - Petrovskii-Piskunov构造一个新的解。为了解决这一问题,采用了非线性偏微分方程的直接Hirota法。介绍了对该方法的一些改进。明确构造了改进的Fisher-Kolmogorov-Petrovskii-Piskunov方程的新的拓扑非平凡解。这个解有一个类似扭结的形式。对该解的稳定性进行了讨论。证明了用Fisher-Kolmogorov - Petrovskii-Piskunov方程描述的系统形成域结构的可能性。
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Domain Structure Formation in Designing of the Opened Informative Measuring Systems
The opened systems possess an increasing significance and possibilities of applying in designing of measuring devices. Now an essentially nonlinear models are used for such systems. The perturbation approach is not enough for these purposes. Models of new types have solutions in a form of soliton or kink and similar objects. The equation of Fisher–Kolmogorov–Petrovskii–Piskunov is one of such equations. This equation is used for description of convection-reaction-diffusion processes. Such processes are used for studying of a self-organisation and formation of a structure in non-equilibrium opened systems. The aim of this work was to construct of a new solution for the modified equation of Fisher–Kolmogorov– Petrovskii–Piskunov in which a space inhomogeneity is accounted.To solve this problem the direct Hirota method for nonlinear partial differential equation is applied.Some modifications into this method were introduced.The new topologically non-trivial solution of the modified Fisher–Kolmogorov–Petrovskii–Piskunov equation is constructed explicitly. This solution has a kink-like form. Some arguments on the stability of such solution are considered.A possibility of domain structure formation in the systems which describe by the Fisher–Kolmogorov– Petrovskii–Piskunov equation is demonstrated. 
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来源期刊
Devices and Methods of Measurements
Devices and Methods of Measurements INSTRUMENTS & INSTRUMENTATION-
自引率
25.00%
发文量
18
审稿时长
8 weeks
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