Pfaffian solutions and nonlinear waves of a (3 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics

Abstract

Fluid mechanics is concerned with the behavior of liquids and gases at rest or in motion, where the nonlinear waves and their interactions are important. Hereby, we study a (3 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics. We determine a bilinear form of that system via the Hirota method. Nth-order Pfaffian solutions are obtained via the Pfaffian technique and our bilinear form, where N is a positive integer. Based on the Nth-order Pfaffian solutions, we derive the N-soliton, higher-order breather, and hybrid solutions. Using those solutions, we present the (1) elastic interaction between the two solitary waves with a short stem, (2) elastic interaction between the two solitary waves with a long stem, (3) fission between the two solitary waves, (4) fusion between the two solitary waves, (5) one breather wave, (6) elastic interaction between the two breather waves, (7) fission between the two breather waves, (8) fusion among the one breather wave and two solitary waves, and (9) elastic interaction between the one breather wave and one solitary wave.