Painleve analysis of travelling wave solutions and analysis of energy estimates for a nonlinear Sobolev-type equation
https://doi.org/10.26907/2541-7746.2023.3.182-189
Abstract
There is considerable interest in studying unbounded solutions of nonlinear partial equations. In many cases, energy estimates can be used to prove that the solution tends to infinity in finite time, while also providing an estimate for the latter. Here, an equation in which energy estimates fail to gauge the cases when solutions exhibit such behavior was analyzed. A class of unbounded solutions was explored using the Painleve analysis.
Supporting agencies: This study was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center of Fundamental and Applied Mathematics (agreement no. 075-15-2022-284).
About the Author
A. I. Aristov
Lomonosov Moscow State University; Federal Research Center “Computer Sciences and Control”, Russian Academy of Sciences; MIREA – Russian Technological University
Russian Federation
Russian Federation
Moscow, 119991
Moscow, 119333
Moscow, 119454
References
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Review
For citations:
Aristov A.I. Painleve analysis of travelling wave solutions and analysis of energy estimates for a nonlinear Sobolev-type equation. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2023;165(3):182-189. (In Russ.) https://doi.org/10.26907/2541-7746.2023.3.182-189
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