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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 206, Number 3, Pages 384–399
DOI: https://doi.org/10.4213/tmf9991 (Mi tmf9991) 		 
Soliton-like excitations in weakly dispersive media

A. S. Kovalevab

a Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine
b Karazin Kharkiv National University, Kharkov, Ukraine
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DOI: https://doi.org/10.4213/tmf9991
Abstract: We consider the question of the possible existence of two-parameter envelope solitons in weakly dispersive media with an acoustic spectrum of linear waves. We propose an asymptotic procedure for finding such soliton solutions in the one-dimensional case and demonstrate the proposed method in the example of the modified Boussinesq equation. We study the question of nonlinear multidimensional localization of excitations in weakly dispersive media with an acoustic spectrum of linear waves.
Keywords: linear wave dispersion law, nonlinear wave, envelope soliton, Fourier series, power series expansion, asymptotic expansion.
Funding agency Grant number
National Academy of Sciences of Ukraine 4.17-Н
1.4.10.26/Ф-26-4
This research is supported by the National Academy of Sciences of Ukraine (Project No. 4.17-N) and the scientific program 1.4.10.26/F-26-4.
Received: 06.10.2020
Revised: 03.11.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 206, Issue 3, Pages 335–348
DOI: https://doi.org/10.1134/S0040577921030065
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. S. Kovalev, “Soliton-like excitations in weakly dispersive media”, TMF, 206:3 (2021), 384–399; Theoret. and Math. Phys., 206:3 (2021), 335–348
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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