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TMF, 2018, Volume 195, Number 3, Pages 362–380 (Mi tmf9421)  

Regular and irregular solutions in the problem of dislocations in solids

S. A. Kashchenkoab

a Demidov Yaroslavl State University, Yaroslavl, Russia
b National Research Nuclear University "MEPhI", Moscow, Russia

Abstract: For an initial differential equation with deviations of the spatial variable, we consider asymptotic solutions with respect to the residual. All solutions are naturally divided into classes depending regularly and irregularly on the problem parameters. In different regions in a small neighborhood of the zero equilibrium state of the phase space, we construct special nonlinear distribution equations and systems of equations depending on continuous families of certain parameters. In particular, we show that solutions of the initial spatially one-dimensional equation can be described using solutions of special equations and systems of Schrödinger-type equations in a spatially two-dimensional argument range.

Keywords: bifurcation, stability, normal form, singular perturbation, dynamics.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.12873.2018/12.1
This research was supported by the Russian Federation Ministry of Education and Science in the framework of state assignment No. 1.12873.2018/12.1.


DOI: https://doi.org/10.4213/tmf9421

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English version:
Theoretical and Mathematical Physics, 2018, 195:3, 807–824

Bibliographic databases:

Document Type: Article
Received: 19.06.2017
Revised: 29.08.2017

Citation: S. A. Kashchenko, “Regular and irregular solutions in the problem of dislocations in solids”, TMF, 195:3 (2018), 362–380; Theoret. and Math. Phys., 195:3 (2018), 807–824

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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