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In this paper, we report on the generation and propagation of travelingpulses in a homogeneous network of diffusively coupled, excitable, slow-fastdynamical neurons. The spatially extended system is modelled using the nearestneighbor coupling theory, in which the diffusion part measures the spatialdistribution of the coupling topology. We derive analytically the conditionsfor traveling wave profiles that allow the construction of the shape oftraveling nerve impulses. The analytical and numerical results are used toexplore the nature of the propagating pulses. The symmetric or asymmetricnature of the traveling pulses is characterized and the wave velocity isderived as a function of system parameters. Moreover, we present our resultsfor an extended excitable medium by considering a slow-fast biophysical modelwith a homogeneous, diffusive coupling that can exhibit various travelingpulses. The appearance of series of pulses is an interesting phenomenon frombiophysical and dynamical perspective. Varying the perturbation and couplingparameters, we observe the propagation of activities with various amplitudemodulations and transition phases of different wave profiles that affect thespeed of the pulses in certain parameter regimes. We observe different types oftraveling pulses, such as envelope solitons and multi-bump solutions and showhow system parameters and the coupling play a major role in the formation ofdifferent traveling pulses. Finally, we obtain the conditions for stable andunstable plane waves.

The generation of diverse traveling pulses and its solution scheme in an excitable slow-fast dynamics