Regular and Irregular Solutions in the Problem of Dislocations in Solids

被引:0
作者
S. A. Kashchenko
机构
[1] National Research Nuclear University “MEPhI,Demidov Yaroslavl State University, Yaroslavl, Russia
[2] ”,undefined
来源
Theoretical and Mathematical Physics | 2018年 / 195卷
关键词
bifurcation; stability; normal form; singular perturbation; dynamics;
D O I
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中图分类号
学科分类号
摘要
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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页码:807 / 824
页数:17
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共 27 条
[1]  
Kontorova T. A.(1938)On the theory of plastic deformation and twinning I Sov. JETP 8 89-97
[2]  
Frenkel’ Y.a. J.(1938)On the theory of plastic deformation and twinning II Sov. JETP 8 1340-1348
[3]  
Kontorova T. A.(1938)On the theory of plastic deformation and twinning III Sov. JETP 8 1349-1358
[4]  
Frenkel’ Y.a. J.(2012)Packets of resonant modes in the Fermi–Pasta–Ulam system Phys. Lett. A 376 2038-2044
[5]  
Kontorova T. A.(1967)Method for solving the Korteweg–deVries equation Phys. Rev. Lett. 19 1095-1097
[6]  
Frenkel’ Y.a. J.(2016)From the Fermi–Pasta–Ulam model to higher-order nonlinear evolution equations Rep. Math. Phys. 77 57-67
[7]  
Genta T.(2016)Two wave interactions in a Fermi–Pasta–Ulam model Model. Anal. Inform. Sist. 23 548-558
[8]  
Giorgilli A.(1996)Normalization in the systems with small diffusion Internat. J. Bifur. Chaos 6 1093-1109
[9]  
Paleari S.(2015)Local dynamics of the two-component singular perturbed systems of parabolic type Internat. J. Bifur. Chaos 25 1550142-513
[10]  
Penati T.(1988)Quasinormal forms for parabolic equations with small diffusion Soviet Math. Dokl. 37 510-870