Novel multiple solitons, their bifurcations and high order breathers for the novel extended Vakhnenko–Parkes equation

Abstract

This paper presents a rigorous exploration of the extended Vakhnenko–Parkes-Equation (eVPE), unveiling a rich tapestry of multi solitons, bifurcations, and high-order breathers. Notably, it achieves an impressive feat by deriving solitons up to sixth order and breathers up to third order, pushing the boundaries of the equation’s solutions. These intricate solutions are not only derived but also vividly brought to life through numerical visualizations, underscoring the profound implications of the our work. Through insightful discussions, the manuscript effectively underscores the significance of these findings, opening new avenues for understanding nonlinear dynamics and their applications across various scientific domains.

Keywords

• Multi solitons
• Bifurcations
• Breathers
• Extended Vakhnenko–Parkes-Equation