Darboux-Bäcklund transformation, breather and rogue wave solutions for the discrete Hirota equation

Abstract

Based on the Lax pair, the pseudopotential and Darboux-Bäcklund transformation of the discrete Hirota equation are given, from which a generalized form of nonlinear wave solutions is derived. By analyzing the properties of the pseudopotential, various types of localized wave solutions including n-direction, t-direction breather wave and rational solutions are obtained and the corresponding dynamical properties and evolutions are given. The obtained results may raise the possibility of related experiments and potential applications in nonlinear science fields, such as nonlinear optics, Bose-Einstein condensates and so on.