Soliton dynamics and multistability analysis of the Hamiltonian amplitude model

Abstract

This work delivers the soliton outcomes through the 1G′ scheme, the modified extended tanh-function (METF) method, and the 1G,G′G approach to the Hamiltonian amplitude (HA) model. The multiple bright dark breather waves with singular solution, bright dark breather waves with singularity, periodic waves, double periodic waves, dark soliton, and bright soliton are formed from this system with the help of the above three techniques via computer software. 2D phase portraits and Poincaré plots study the multistability of the mentioned model. Furthermore, a comparison is shown between this research and some recently published work to check the uniqueness of this research. In addition, 3D curves with density plots and 2D diagrams represent the behavior of solitons. The conclusions of this study have implications for further research in this field. The study also provides a better understanding of the behavior of solitons.