Jacobian elliptic wave trains in fourth-order dispersive nonlinear Schrödinger equation and the modulational instability

Abstract

We analytically and numerically explore the existence of explicit exact Jacobian elliptic solutions of a nonlinear Schrödinger model with fourth-order dispersion and weak nonlocality. We delineate the parameter domain in which these highly dispersive doubly periodic waves balanced by the weak nonlocality and Kerr nonlinearity exist. Additionally, we have studied the modulational instability (MI) of these waves with the aid of linear stability analysis. We observe that in the presence of fourth-order dispersion, the MI gain increases with increasing the nonlocality parameter.