Pfaffian, breather, and hybrid solutions for a (2 <b>+</b> 1)-dimensional generalized nonlinear system in fluid mechanics and plasma physics

Abstract

Fluid mechanics is seen as the study on the underlying mechanisms of liquids, gases and plasmas, and the forces on them. In this paper, we investigate a (2 + 1)-dimensional generalized nonlinear system in fluid mechanics and plasma physics. By virtue of the Pfaffian technique, the Nth-order Pfaffian solutions are derived and proved, where N is a positive integer. Based on the Nth-order Pfaffian solutions, the first- and second-order breather solutions are obtained. In addition, Y-type and X-type breather solutions are constructed. Furthermore, we investigate the influence of the coefficients in the system on those breathers as follows: The locations and periods of those breathers are related to δ1, δ2, δ3, δ4, and δ5, where δc's (c=1,2,3,4,5) are the constant coefficients in the system. Moreover, hybrid solutions composed of the breathers and solitons are derived. Interactions between the Y/X-type breather and Y-type soliton are illustrated graphically, respectively. Then, we show the influence of the coefficients in the system on the interactions between the Y/X-type breather and Y-type soliton.