Eur. Phys. J. Plus (2021) 136: 917
https://doi.org/10.1140/epjp/s13360-021-01828-8

Regular Article

Painlevé analysis, bilinear form, Bäcklund transformation, solitons, periodic waves and asymptotic properties for a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China

^b tian_bupt@163.com

Received: 24 February 2021
Accepted: 31 July 2021
Published online: 7 September 2021

Abstract

In this paper, the investigation is conducted on a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma. We conduct the Painlevé analysis and find that it fails to pass the Painlevé test. Bilinear form, Bäcklund transformation and soliton solutions are derived with the help of the Hirota method. By means of the Riemann theta function method, we obtain the one-periodic wave solutions. We derive the amplitude, velocity and direction of propagation for the one soliton, and find that the coefficients in the system affect the velocities of the one/two solitons, but the amplitudes and propagation directions of the one/two solitons keep unchanged. We graphically demonstrate that the interaction between the two solitons is elastic and analyse the effects of the coefficients in the system on the solitons and periodic waves. We analyse the asymptotic properties of the one-periodic wave solutions which reveal the connection between the one-periodic wave solutions and the one-soliton solutions, i.e., the one-periodic wave solutions tend to the one-soliton solutions under the limit process.