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 Schr¨odinger-type equations in a spatially two-dimensional argument range.
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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.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 195, No. 3, pp. 362–380, June, 2018.
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Kashchenko, S.A. Regular and Irregular Solutions in the Problem of Dislocations in Solids. Theor Math Phys 195, 807–824 (2018). https://doi.org/10.1134/S0040577918060028
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DOI: https://doi.org/10.1134/S0040577918060028