Traveling wave solution and qualitative behavior of fractional stochastic Kraenkel–Manna–Merle equation in ferromagnetic materials

The main purpose of this article is to investigate the qualitative behavior and traveling wave solutions of the fractional stochastic Kraenkel–Manna–Merle equations, which is commonly used to simulate the zero conductivity nonlinear propagation behavior of short waves in saturated ferromagnetic mate...

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Bibliographic Details
Published in:Scientific reports 2024-06, Vol.14 (1), p.12990-7
Main Author: Luo, Jie
Format: Article
Language:English
Subjects:
639/766/259
639/766/530/2803
Behavior
Bifurcation
Brownian motion
Differential equations
Dynamical systems
Equilibrium
Humanities and Social Sciences
Kraenkel–Manna–Merle equations
multidisciplinary
Ordinary differential equations
Partial differential equations
Phase portrait
Plane dynamics system
Science
Science (multidisciplinary)
Sensitivity analysis
Stochasticity
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Summary:The main purpose of this article is to investigate the qualitative behavior and traveling wave solutions of the fractional stochastic Kraenkel–Manna–Merle equations, which is commonly used to simulate the zero conductivity nonlinear propagation behavior of short waves in saturated ferromagnetic materials. Firstly, fractional stochastic Kraenkel–Manna–Merle equations are transformed into ordinary differential equations by using the traveling wave transformation. Secondly, the phase portraits, sensitivity analysis, and Poincaré sections of the two-dimensional dynamic system and its perturbation system of ordinary differential equations are drawn. Finally, the traveling wave solutions of fractional stochastic Kraenkel–Manna–Merle equations are obtained based on the analysis theory of planar dynamical system. Moreover, the obtained three-dimensional graphs of random solutions, two-dimensional graphs of random solutions, and three-dimensional graphs of deterministic solutions are drawn.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-024-63714-4