Comment on “Dynamical behavior and modulation instability of optical solitons in nonlinear directional couplers”

Recently, Liu et al. [Nonlinear Dyn (2023) 111:10441–10458] have considered a coupled dissipative nonlinear Schrödinger equations that model the dynamics of optical nonlinear waves in nonlinear directional couplers. Applying the linear stability analysis method, they investigated the modulational instability of constant amplitude plane wave solutions of their model equations. Unfortunately, the coupled dissipative nonlinear Schrö dinger equations considered in their study does not admit any plane wave solution with constant amplitude when either \(\left| \alpha _{1}\right| +\left| \alpha _{2}\right| >0\) $\left|{\alpha }_1\right|+\left|{\alpha }_2\right|>0$ or \(\eta \ne 1\) $\eta \ne 1$ . Moreover, the ansatz used for the perturbation in their work is inappropriate for investigating the modulational instability phenomenon. The aim of the present comment is to prove that the research work conducted by Liu et al. in “Dynamical behavior and modulation instability of optical solitons in nonlinear directional couplers” should not be considered accurate. We start the present comment by presenting all shortcomings of the results found by Liu et al. on the modulational instability. Then, we employ the method of the dynamical system to investigate the modulational instability of the zero amplitude wave solution of their model equations.