Wen-Xiu Ma, “A combined generalized Kaup–Newell soliton hierarchy and its hereditary recursion operator and bi-Hamiltonian structure”, TMF, 2024, Volume 221, Number 1,Pages <nobr>18

This article is cited in 27 papers

A combined generalized Kaup–Newell soliton hierarchy and its hereditary recursion operator and bi-Hamiltonian structure

Wen-Xiu Ma^abcd

^a Department of Mathematics, Zhejiang Normal University, Zhejiang, China
^b Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
^c Department of Mathematics and Statistics, University of South Florida, Tampa, USA
^d Material Science Innovation and Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho, South Africa

Abstract: On the basis of a specific matrix Lie algebra, we propose a Kaup–Newell-type matrix eigenvalue problem with four potentials and compute an associated soliton hierarchy within the zero-curvature formulation. A hereditary recursion operator and a bi-Hamiltonian structure are presented to show the Liouville integrability of the resulting soliton hierarchy. An illustrative example is a novel model consisting of combined derivative nonlinear Schrödinger equations with two arbitrary constants.

Keywords: matrix eigenvalue problem, zero-curvature equation, integrable hierarchy, derivate nonlinear Schrödinger equations.

PACS: 02.30.Ik, 05.45.Yv

MSC: 37K15, 35Q55

Received: 28.02.2024
Revised: 28.02.2024

DOI: 10.4213/tmf10712