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

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.

Automated summary

This paper investigates the dynamical behavior of high-frequency waves in the relaxation medium using the Vakhnenko-Parkes and modified Khater methods, resulting in numerous novel solitary wave solutions and demonstrating the accuracy of solutions. The methods' performance is shown to be effective, direct, easy, and beneficial for studying various nonlinear evolution equations.