LAUSR

Abstract The perturbed Boussinesq equation and the KdV-Caudrey-Dodd-Gibbon equation describe the characteristics of longitudinal waves in bars, long water waves, plasma waves, quantum mechanics, acoustic waves, nonlinear optics etc. Thus, the mentioned equations are clearly important in their own right. In this article, the modified auxiliary equation technique has been put in use in order to ascertain exact soliton solutions to the stated nonlinear evolution equations (NLEEs). We determine adequate soliton solutions, explicitly, bell-shaped soliton, kink-soliton, periodic-wave, singular-kink, compacton-soliton and other types. These solutions might play an important role in uncovering the underlying context of the physical incidents. It is noteworthy that the executed method is skilled and effective to examine NLEEs, compatible with computer algebra and provides wide-ranging wave solutions. Thus, the study of exact solutions to other NLEEs through the modified auxiliary equation method is prospective and deserves further research.