Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics

Abstract

In this paper, a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics is studied. Bilinear form under certain constraints is given via the Hirota method. The Nth-order Pfaffian solutions are proved via the Pfaffian technique, where N is a positive integer. N-soliton and the higher-order breather solutions are derived from the Nth-order Pfaffian solutions. Y/X-type solitons are constructed via adding some conditions to the N-soliton solutions. Elastic and inelastic interactions between the two solitons are presented graphically. Y/X-type breathers are constructed via adding some conditions to the higher-order breather solutions. Y-type breathers describe the inelastic interactions between the two breathers, and the X-type breathers describe the different two-breather structure. We investigate the influence of the coefficients in the system on those solitons and breathers as follows: the amplitudes of those solitons and breathers are related to l1 and l2; the periods of those breathers are related to l1, l2, l3 and l5, where l1, l2, l3 and l5 are the constant coefficients in the system.