Dynamics of chirped solitary waves: bifurcation and chaos in nonlinear chains with Morse potential

In this study, we explore the bifurcation of chirped waves in a nonlinear lattice incorporating the Morse potential. By applying the reductive perturbation method, we derive the generalized Kaup-Newell equation, representing the nonlinear system in a planar framework. Through qualitative analysis, homoclinic and heteroclinic orbits are revealed, confirming the propagation of solitary waves, including envelope solitons, dark solitons, kink, double-kink solutions, and periodic waves within the nonlinear chain. Furthermore, the introduction of an external force highlights chaotic behaviors, quasi-regular patterns, and time-dependent waveforms within the system. Notably, the qualitative characteristics exhibit extreme sensitivity to variations in the external force's amplitude. Additionally, the generalized Kaup-Newell model is derived from the nonlinear Klein–Gordon equation, providing further insight into the bifurcation behavior of solitary waves.