Abundant breather and semi-analytical investigation: On high-frequency waves’ dynamics in the relaxation medium

Abstract

This paper investigates the high-frequency waves’ dynamical behavior in the relaxation medium through two recent analytical schemes. This study depends on the Vakhnenko–Parkes (VP) equation that has been reduced from the well-known Ostrovsky equation. The modified Khater (MKhat) and the extended simplest equation (ESE) methods are used to handle the considered model. As a result, many novel solitary wave solutions have been obtained to construct the initial and boundary conditions. These conditions allow employing the variational iteration (VI) method to study the semi-analytical solutions of the considered model. The accuracy of solutions is explained along with showing the matching between analytical and semi-analytical solutions and comparing our obtained solutions with the previous results that have been obtained in published research papers. Moreover, the high-frequency waves’ behavior relaxation medium is illustrated through some distinct sketches. The methods’ performance shows their effectiveness, direct, easy, and consequential for studying many nonlinear evolution equations.