Hamiltonian structure and soliton solutions for Konno-Oono equation with self-consistent sources

Abstract

In this paper, we investigate the system of Konno-Oono equation with self-consistent sources. The aim of this research is to determine the conserved quantities (Hamiltonians) from the Riccati equations for the Konno- Oono system with self-consistent sources and to obtain one-soliton solutions using Hirota's bilinear method. This model provides an idealized description of how short pulses propagate in magnetic fields and in various physical contexts, including nonlinear waves, optics, and hydrodynamics. We obtain Lax pairs and an integrability condition for systems of Konno - Oono equations. We derive its Hamiltonian structure by expanding the spectral parameter into inverse powers, resulting in an infinite hierarchy of conserved quantities expressed in terms of smooth real functions and their derivatives. We use the Hirota bilinear method to construct soliton solutions. By introducing transformations of the dependent variables and expanding them into power series, we obtain one-soliton solutions for the fields q, ρ, p, and η. We construct graphical representations of localized stable wave profiles characteristic of solitons in such systems.