A new trial equation method for finding exact chirped soliton solutions of the quintic derivative nonlinear Schrödinger equation with variable coefficients

Abstract

In this work, we propose an efficient generalization of the trial equation method introduced recently by Liu [Appl. Math. Comput. 217 (2011) 5866] to construct exact chirped traveling wave solutions of complex differential equations with variable coefficients. The effectiveness of the proposed method has been tested by applying it successfully to the quintic derivative nonlinear Schrödinger equation with variable coefficients. As a result, a class of chirped soliton-like solutions including bright and kink solitons is derived for the first time. Compared with previous work of Liu in which unchirped solutions were given, we obtain exact chirped solutions which have nontrivial phase that varies as a function of the wave intensity. These localized structures characteristically exist due to a balance among the group-velocity dispersion, self-steepening and competing cubic-quintic nonlinearity. Parametric conditions for the existence of envelope solutions with nonlinear chirp are also presented. It is shown that the chirping can be effectively controlled through the variable parameters of group-velocity dispersion and self-steepening.