Dynamics of modulated waves in a dissipative nonlinear network with nonlinear dispersion

•Dissipation and nonlinear dispersion limit the experimental observation of the Modulational Instability phenomenon.•Dissipation and nonlinear dispersion can be used to manage the amplitude and the width of solitonlike waves of the network.•Increasing the nonlinear dispersion parameter decreases both the width and the amplitude of solitonlike waves of the network.•Increasing the dissipative losses in the network increases the wave amplitude and decreases its width.

In this present paper, we investigate analytically the dynamics of modulated waves in a dissipative nonlinear network with nonlinear dispersion. In the small amplitude limit, we use the reductive perturbation method and the continuum limit approximation to derive an envelope Ginzburg-Landau (GL) equation of the network. Considering modulated Stokes waves propagating in the network, we investigate their modulational instability (MI) and derive the analytical expression for the instability growth rate. We show that both the dissipative losses and the nonlinear dispersion constitute a great limiting factor to the experimental observation of the MI phenomenon. Investigating the transmission of modulated waves through the network, we show that the amplitude and the width of the solitonlike waves propagating in the network can be managed with the use of both the dissipative losses and the nonlinear dispersion of the network.