Geodesic
Regular and irregular solutions in the~problem of dislocations in solids
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 362-380

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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.
Mots-clés : bifurcation, singular perturbation
Keywords: stability, normal form, dynamics. 
@article{TMF_2018_195_3_a1,
     author = {S. A. Kashchenko},
     title = {Regular and irregular solutions in the~problem of dislocations in solids},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {362--380},
     publisher = {mathdoc},
     volume = {195},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a1/}
}
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S. A. Kashchenko. Regular and irregular solutions in the~problem of dislocations in solids. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 362-380. http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a1/