Solitons and breather waves for the generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics, ocean dynamics and plasma physics

•The Nth-order Pfaffian and Wronskian solutions are derived via the Pfaffian and Wronskian techniques, respectively.•One-and two-soliton solutions are constructed via the Nth-order solutions.•Asymptotic analysis implies that the interaction between the two solitons is elastic with certain conditions.•Breather waves have been obtained according to the extended homoclinic test technique.•Propagation of the breather waves indicates that the breather waves can evolve periodically along a straight line with a certain angle with the x and y axes, and their wave lengthes, amplitudes and velocities remain unchanged during the propagation. Under investigation in this paper is the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system, which can be used to describe certain situations in fluid mechanics, ocean dynamics and plasma physics. The Nth-order Pfaffian and Wronskian solutions are derived via the Pfaffian and Wronskian techniques, respectively, where N is a positive integer. Asymptotic analysis implies that the interaction between the two solitons is elastic with certain conditions. Furthermore, we obtain the breather waves according to the extended homoclinic test technique. Propagation of the breather waves indicates that the breather waves can evolve periodically along a straight line with a certain angle with the x and y axes, and their wave lengthes, amplitudes and velocities remain unchanged during the propagation.