Two-component nonlinear wave solutions of the sixth-order generalised Boussinesq-type equations
Exactly Solvable and Integrable Systems
2025-03-05 v1 Mesoscale and Nanoscale Physics
Pattern Formation and Solitons
Abstract
Two different versions of cubic sixth-order generalised Boussinesq-type wave equations are considered in this study. A generalised perturbation reduction method is used to solve these equations, which allows the reduction of considered equations to coupled nonlinear Schrodinger equations. Two-component nonlinear wave solutions are obtained. The profiles and parameters of these solutions for both nonlinear equations are presented and compared. These solutions coincide with the vector 0 \pi pulse of self-induced transparency, which was previously studied in several known nonlinear wave equations.
Keywords
Cite
@article{arxiv.2503.02576,
title = {Two-component nonlinear wave solutions of the sixth-order generalised Boussinesq-type equations},
author = {G. T. Adamashvili},
journal= {arXiv preprint arXiv:2503.02576},
year = {2025}
}