The bi-Hamiltonian structure and new solutions of KdV6 equation

Abstract

We show that the KdV6 equation recently studied in [1,2] is equivalent to the Rosochatius deformation of KdV equation with self-consistent sources (RD-KdVESCS) recently presented in [9]. The $t$-type bi-Hamiltonian formalism of KdV6 equation (RD-KdVESCS) is constructed by taking $x$ as evolution parameter. Some new solutions of KdV6 equation, such as soliton, positon and negaton solution, are presented.

arXiv comment13 pages

References in corpus (6)

• KdV6: An Integrable System
• A new integrable generalization of the Korteweg - de Vries equation
• Quasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHRÖdinger Equations
• Negaton and Positon solutions of the soliton equation with self-consistent sources
• Exact accelerating solitons in nonholonomic deformation of the KdV equation with two-fold integrable hierarchy
• Integrable Rosochatius deformations of higher-order constrained flows and the soliton hierarchy with self-consistent sources

Cited by in corpus (4)

• Dynamical study of nonlinear ion-acoustic waves in presence of charged space debris at Low Earth Orbital (LEO) plasma region
• The generalized Kupershmidt deformation for constructing new integrable systems from integrable bi-Hamiltonian systems
• On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources
• The generalized Kupershmidt deformation for constructing new discrete integrable systems