Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation

Abstract

Abstract The generalized nonlocal nonlinear Hirota (GNNH) equation has been widely concerned, it can be regarded as the generalization of the nonlocal Schrödinger equation, and can be reduced to a nonlocal Hirota equation. In this paper, we mainly study a GNNH equation and its determinant representation of the N-fold Darboux transformation. Then we derive some novel exact solutions including the breather wave solitons, bright solitons, some characteristics of solitary wave and interactions are considered. In particularly, the dynamic features of one-soliton, two-soliton solutions and the elastic interactions between the two solitons are displayed. We find that unlike the local case, the q(x,t) and q ∗ ( − x , t ) $q^{*}(-x,t)$ of the GNNH equation have some novel characteristics of solitary wave, which are different form the classical Hirota equation.