Stability analysis and soliton solutions to the new Hamiltonian amplitude equation in mathematical physics

Abstract The new Hamiltonian amplitude (nHA) equation deals with some of the disabilities of the modulation wave-train. The main task of this paper is to extract the analytical wave solutions of the nHA equation. Based on the unified scheme, analytical wave solutions are attained in terms of hyperbolic and trigonometric function solutions. In order to prompt the underlying wave propagation characteristics, three-dimensional (3D), two-dimensional (2D) are illustrated from the solutions obtained with the help of computational packages Mathematica and also made comparisons between wave profiles for various values. The proposed method can also be used for many other nonlinear evolution equations.