https://doi.org/10.1140/epjp/s13360-024-04951-4
Regular Article
The traveling wave solutions for generalized Benjamin–Bona–Mahony equation
School of Data-Science and Information-Engineering, Guizhou Minzu University, 550025, Guizhou, Guiyang, People’s Republic of China
a
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Received:
11
April
2023
Accepted:
26
January
2024
Published online:
4
March
2024
Abstract
The traveling wave solutions of generalized BBM equation with any power are investigated. The existence and numbers of bell solitary wave solutions, kink solitary wave solutions and periodic wave solutions are obtained by using qualitative theory of planar dynamical system. The new exact expressions of peaked light solitary wave solutions, valley dark solitary wave solutions and kink solitary wave solutions are given by the method of undetermined coefficient. Further, by numerical simulating, the behavior of these exact traveling solutions are analyzed. In visually, we verify that the result about existence of traveling wave solutions for generalized BBM equation is right. Moreover, the convexity, monotonicity and number of critical points for period solutions of generalized BBM equation have been discussed. The integral expressions and corresponding orbit curves of period solutions are studied.
This project is supported by Fund of the Natural Science Research Project of Department of Education of Guizhou Province (Grant No.QJJ2023012,QJJ2023061,QJJ2023062 QJJ2022015,QJJ2022047) and National Natural Science Foundation of China (Grant No.12361083, 11961009).
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
