Characteristics of solitary waves, breather waves and hybrid waves to a new (3 + 1)-dimensional nonlinear evolution equation in a quantum magnetoplasma

Abstract

By considering the nonlinear propagations of electron acoustic waves in quantum magnetoplasmas, we successfully derive a new ()-dimensional nonlinear evolution equation (NLEE) via the standard reductive perturbation theory. Through introducing a suitable transformation, the Hirota's bilinear equation of the ()-dimensional NLEE is first found analytically. Some interesting mathematical analytical results are further investigated, including some dynamics of solitary waves, breather waves, and hybrid waves. Based on the resulting bilinear form, an effective method is presented to find its N-solitary wave solutions. Moreover, by taking particular complex conjugate conditions, we further obtain its N-th–order breather wave solutions and general hybrid wave solutions which have not been reported yet. Finally, some significant characteristics of these nonlinear waves are illustrated to better understand their dynamical behavior. For these analytic solutions, the influences of each parameter on the dynamics of solitary waves, breather waves, and hybrid waves are discussed, and the method of how to control such nonlinear waves is also suggested.