In this paper, the fourth-order Cahn–Hilliard equation is studied, which plays an important role in the development of the spinodal decomposition, phase separation, and phase ordering dynamics. The \(\tan (\phi /2)\) -expansion method (TEM), Jacobi elliptic function expansion scheme (JEFES), rational multi wave functions (RMWFs), and decomposition variational iteration method (DVIM) are considered to investigate the exact traveling wave solutions to nonlinear evolution equations (NLEEs) in the domain of applied physics and engineering. This equation can be utilized to explain the contact between the modes in describing the process of phase separation of a binary alloy under the critical temperature, phase separation, phase-ordering dynamics, and spinodal decomposition, fluid mechanics, and fluid flow. The dynamics of the assessed solutions in terms of understanding the real phenomena for such nonlinear model is demonstrated by plotting their 3D, 2D, contour, and density profiles using proper parametric values. Consequently, we obtain distinct types of solutions, containing dark, bright, kink, singular, combo kink singular, and combo dark singular soliton solutions. These results are essential to the explanation of several mesmerizing and intricate physical phenomena. Also, the decomposition variational iteration method of the proposed model is analyzed and conditions are developed accordingly. The soliton solutions demonstrate the competency of the proposed technique in identifying traveling wave solutions, offering a useful tool for tackling a variety of NLEEs. We believe that our results would pave a way for future research generating optical memories based on the nonlinear solitons.
