Study of multi solitons, breather soliton structures in the earth's magnetotail region

Abstract

The investigation of wave packets with varying magnitudes, which predominantly carry energy across different physical mediums, proves to be highly intriguing and unveils numerous nonlinear characteristics within Earth's magnetotail region and magnetosphere, as confirmed by extensive space observations. Nonlinear features in wave dynamics are elucidated through diverse nonlinear structures, among which breather structures hold prominence and manifest across various wave fields. We have considered an unmagnetized collisionless homogeneous hydrodynamical governing equations set in an electron-ion plasma comprising hot and cold ions. In this study, we have explored 1-soliton, 2-soliton, and breather structures in the framework of the Gardner equation (GE). We have derived the GE from the normalized set of governing equations employing the reductive perturbation technique (RPT). The GE, an extension of the Korteweg-de Vries (KdV) equation, encompasses the combined effects of quadratic and cubic nonlinearities. By employing the Hirota bilinear method (HBM), we have obtained multi-soliton solutions and breather soliton solutions. We have noticed the variations in electron temperature ratios and density concentration ratios substantially impact and reshape breather soliton structures. Such alterations in breather structures, influenced by different electron temperatures and concentration ratios, hold potential significance in understanding energy transport within Earth's magnetotail region. The alteration of shapes and soliton structures may also be investigated in the dynamics of wave fields upon interaction such as hydrodynamics, optics, optic fibers, signal processing, etc.