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

Abstract We investigate the bifurcation of the chirped waves in the nonlinear lattice where the Morse potential is used. Using the reductive perturbation method, the generalized Kaup-Newell equation is derived to display the nonlinear system in a planar form. Throughout the qualitative investigations, the homoclinic and heteroclinic orbits have been displayed to confirm the propagation of solitary waves where envelope soliton, dark, kink, and double-kink including the periodic waves in the nonlinear chain fulfilled. Additionally, an external strength is used to shed light on the chaotic, quasi-regular, and time-depend waveforms attitude inside the nonlinear system. One can notice that, the qualitative investigations are extremely sensitive to changes in the amplitude of the outer strength. At the same time, the generalized Kaup-Newell model is also derived from the nonlinear Klein-Gordon equation to throw light on the dynamic behaviors alike to those discovered in models used in Refs. [42, 49, 51, 55].