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

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 delta(1), delta(2), delta(3), delta(4), and delta(5), where delta(c)'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. Published under an exclusive license by AIP Publishing.

Automated summary

This paper investigates a (2 + 1)-dimensional generalized nonlinear system in fluid mechanics and plasma physics, deriving and proving Nth-order Pfaffian solutions using the Pfaffian technique. First- and second-order breather solutions are obtained based on these solutions. Additionally, Y-type and X-type breather solutions are constructed. The influence of the system's coefficients on these breathers is investigated, and hybrid solutions composed of breathers and solitons are derived. Interactions between Y/X-type breathers and Y-type solitons are graphically illustrated, and the influence of the system's coefficients on these interactions is demonstrated.