ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Fakhretdinov M. I., Ekomasov E. G. Kink dynamics in the φ4 model with two extended impurities. Izvestiya VUZ. Applied Nonlinear Dynamics, 2025, vol. 33, iss. 3, pp. 412-425. DOI: 10.18500/0869-6632-003156, EDN: LVTTLP

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Language: 
Russian
Heading: 
Nonlinear Waves. Solitons. Autowaves. Self-Organization.
Article type: 
Article
UDC: 
530.182.1
DOI: 
10.18500/0869-6632-003156
EDN: 
LVTTLP

Kink dynamics in the φ4 model with two extended impurities

Autors: 
Fakhretdinov Marat Irekovich,
Ekomasov Evgenii Grigorievich, Bashkir State University
Abstract: 

The purpose of this study is to use numerical methods to consider the problem of nonlinear kink dynamics for the φ4 equation in a model with two identical extended «impurities» (or spatial inhomogeneity of the potential).

Methods. The φ4 model with inhomogeneities was numerically solved using the method of lines for partial differential equations. The kink was launched in the direction of the inhomogeneities with different initial velocities. The distance between the two impurities was also varied. The kink trajectory after interaction with the impurities was studied. The discrete Fourier transform was used to find the oscillation frequencies of the kink after interaction with spatial inhomogeneities.

Results. The interaction between the kink and two identical extended impurities described by rectangular functions is described. Possible scenarios of kink dynamics are determined, taking into account resonance effects, depending on the magnitude of the system parameters and initial conditions. Critical and resonant velocities of the kink motion are found depending on the impurity parameters and the distance between them. Significant differences are observed in the kink dynamics when interacting with repulsive
and attractive impurities. It is established that among the found scenarios of kink dynamics for the case of extended rectangular impurities, there are scenarios of resonant kink dynamics obtained earlier for the case of one extended impurity, for example, quasi-tunneling and repulsion from an attractive potential.

Conclusion. An analysis of the influence of system parameters and initial conditions on possible scenarios of kink dynamics is carried out. Critical and resonant kink velocities are found as functions of the impurity parameters and the distance between them.

Key words: 
kink
φ4 equation
impurity
numerical simulation
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Received: 
11.11.2024
Accepted: 
27.11.2024
Available online: 
10.12.2024
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