Eur. Phys. J. Plus (2022) 137: 579
https://doi.org/10.1140/epjp/s13360-022-02763-y

Regular Article

Integrability and the multi-soliton interactions of non-autonomous Zakharov–Kuznetsov equation

¹ Department of Mathematics, Cooch Behar Panchanan Barma University, 736101, Cooch Behar, West Bengal, India
² Department of Mathematics, Mathabhanga College, 736164, Cooch Behar, West Bengal, India
³ Department of Mathematics, Siksha Bhavana, Visva-Bharati, 731235, Santiniketan, India

^d prasantachatterjee1@rediffmail.com

Received: 22 February 2022
Accepted: 16 April 2022
Published online: 13 May 2022

Abstract

This manuscript investigates the characteristic of integrability of the Zakharov–Kuznetsov (ZK) equation through the Painlevé analysis in the presence of external periodic forces together with damping, and for the first time, utilizing Hirota’s bilinear method the multiple soliton solutions for non-autonomous ZK equation is explored for different types of forcing components such as trigonometric periodic force, exponentially decaying force and hyperbolic force. It has been found that the autonomous solitons are able to maintain their original shape after their collision. However, in application with the constant damping and externally applied different types of forces, the solitons change their amplitude and direction during their propagation and the background of the solitons remarkably rises when external force increases. It is also observed that the amplitude and velocity of the wave are keenly related to the strength of external forces and damping terms. Furthermore, the soliton interactions of the two or more solitons are examined under the presence of damped term and force perturbation. The propagating characteristics, interaction behaviors with background waves, and phase shifts of the solitons, in particular significant impact from damping and forcing terms in soliton interaction, are analyzed from numerical understanding.