Dynamic waveforms of the new Hamiltonian amplitude model using three different analytic techniques

This manuscript explores the dynamic patterns of the new Hamiltonian amplitude (nHA) model arising in optics, fluid dynamics, plasma physics, and condensed matter physics. We use the unified solver scheme, the novel Kudryashov method, and the modified \(\left(\frac{{G}{\prime}}{{G}^{2}}\right)\)-expansion technique to solve the nHA equation for the first time provides different new dynamic patterns such as bright and dark solitons, multiple and single breather waves with singularity, and periodic and double periodic waves. Three-dimensional with density plots and two-dimensional plots of these outcomes are shown with the help of a computational soft package. To control the parameters, we discuss the stability characteristics for the solution of this model. To prove the novelty of this work, we write a comparison section on this article. These unique outcomes will be vital for the forthcoming investigation of nonlinear equations.