|
Multidimensional nonlinear Klein–Gordon equations and rivertons
V. M. Zhuravlev Kapitsa Technological Research Institute, Ulyanovsk State
University, Ulyanovsk, Russia
Abstract:
Based on solutions of a system of quasilinear first-order equations of a special kind (rivertons), we construct classes of exact solutions of multidimensional nonlinear Klein–Gordon equations. The obtained solutions are expressed in terms of the derivatives of rivertons with respect to the independent variables. As a result, the solutions are multivalued and have singularities at the branch points. In the general case, the solutions can be complex. We establish a relation between the functional form of the nonlinearity of the Klein–Gordon equations and the functional dependence of the solutions on rivertons and their derivatives. We study the conditions under which the nonlinearity of the Klein–Gordon equation has a specific functional form and present examples. We establish a relation between the geometric structure of rivertons and the initial conditions.
Keywords:
multidimensional nonlinear Klein–Gordon equation, multidimensional quasilinear first-order equation, exact solution, riverton.
Funding Agency |
Grant Number |
Russian Foundation for Basic Research  |
16-42-732119 р_офи_м |
Ministry of Education and Science of the Russian Federation  |
3.2111.2017/4.6
|
This work was supported by the Ministry of Education
and Science of the Russian Federation (State Order and Project
No. 3.2111.2017/4.6) and the Russian Foundation for Basic Research (Grant
No. 16-42-732119_a_ofi_m) and in part by the state program of Kazan
University aimed at its performance among the world's leading research and
education centers. |
DOI:
https://doi.org/10.4213/tmf9502
Full text:
PDF file (455 kB)
First page: PDF file
References:
PDF file
HTML file
English version:
Theoretical and Mathematical Physics, 2018, 197:3, 1701–1713
Bibliographic databases:
PACS:
03.65.Ge, 03.65.Pm, 02.30.Jr
MSC: 35L70, 35L40, 81Q05 Received: 02.11.2017 Revised: 30.05.2018
Citation:
V. M. Zhuravlev, “Multidimensional nonlinear Klein–Gordon equations and rivertons”, TMF, 197:3 (2018), 356–370; Theoret. and Math. Phys., 197:3 (2018), 1701–1713
Citation in format AMSBIB
\Bibitem{Zhu18}
\by V.~M.~Zhuravlev
\paper Multidimensional nonlinear Klein--Gordon equations and rivertons
\jour TMF
\yr 2018
\vol 197
\issue 3
\pages 356--370
\mathnet{http://mi.mathnet.ru/tmf9502}
\crossref{https://doi.org/10.4213/tmf9502}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...197.1701Z}
\elib{https://elibrary.ru/item.asp?id=36448160}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 197
\issue 3
\pages 1701--1713
\crossref{https://doi.org/10.1134/S0040577918120024}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000455189700002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059686808}
Linking options:
http://mi.mathnet.ru/eng/tmf9502https://doi.org/10.4213/tmf9502 http://mi.mathnet.ru/eng/tmf/v197/i3/p356
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
|
Number of views: |
This page: | 201 | References: | 33 | First page: | 25 |
|