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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 127, Number 3, Pages 401–410
DOI: https://doi.org/10.4213/tmf468 (Mi tmf468) 		 
Perturbation of Solutions with Moving Singularities

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
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DOI: https://doi.org/10.4213/tmf468
Abstract: We study the Cauchy problem for a nonlinear second-order differential equation with a small parameter in the case where the exact solution has a power singularity depending on a small parameter. We propose an asymptotic method similar to the Krylov–Bogoliubov method for localizing the singularity up to the accuracy of any order and construct an asymptotic expansion of the solution in the domain of regular behavior.
English version:
Theoretical and Mathematical Physics, 2001, Volume 127, Issue 3, Pages 751–759
DOI: https://doi.org/10.1023/A:1010495617211
Bibliographic databases:
Language: Russian
Citation: L. A. Kalyakin, “Perturbation of Solutions with Moving Singularities”, TMF, 127:3 (2001), 401–410; Theoret. and Math. Phys., 127:3 (2001), 751–759
Citation in format AMSBIB
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\pages 401--410
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\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 127
\issue 3
\pages 751--759
\crossref{https://doi.org/10.1023/A:1010495617211}
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