Solitonic wave solutions of a Hamiltonian nonlinear atom chain model through the Hirota bilinear transformation method

Abstract This study employs the Hirota bilinear transformation method to investigate solitary and soliton solutions resulting from different symmetry wave functions associated with nonlinear atom chain models. These models are complex dynamic systems that have an impact on a variety of scientific areas. In this work, we derive exact solutions for several symmetry wave functions. Our results reveal a wide range of wave structures, including anti-kink waves (resulting from the interaction of exponential wave functions), M-shaped waves with single and double kinks (generated by combining M-shaped and kink wave functions), and periodic multiple lump waves (produced by the interaction of multi-lump and periodic wave functions). Solitary waves and numerous periodic lump waves have also been reported as a result of various multi-wave function combinations. In the present report, we also derive periodic bright lump waves, periodic cross-kink waves, and dark lump strip waves caused by interactions between exponential, trigonometric, and hyperbolic functions. Additional solutions include solitary waves from mixed wave functions and bright breather waves obtained from homoclinic breather functions. For illustration purposes, we provide three-dimensional visualizations of these solutions as well as accompanying contour plots.