Wen-Xiu Ma, “Four-component integrable hierarchies of Hamiltonian equations with (<nobr>$m+n+2$</nobr>)th-order Lax pairs”, TMF, 2023, Volume 216, Number 2,Pages <nobr>315

This article is cited in 63 papers

Four-component integrable hierarchies of Hamiltonian equations with ($m+n+2$)th-order Lax pairs

Wen-Xiu Ma^abcd

^a Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China
^b Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
^c Department of Mathematics and Statistics, University of South Florida, Tampa, FL, USA
^d School of Mathematical and Statistical Sciences, North-West University, Mmabatho, South Africa

Abstract: A class of higher-order matrix spectral problems is formulated and the associated integrable hierarchies are generated via the zero-curvature formulation. The trace identity is used to furnish Hamiltonian structures and thus explore the Liouville integrability of the obtained hierarchies. Illuminating examples are given in terms of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations with four components.

Keywords: Lax pair, zero-curvature equation, integrable hierarchy, Hamiltonian structure, NLS equations, mKdV equations.

PACS: 02.30.Ik, 05.45.Yv

MSC: 37K15, 35Q55; 37K40

Received: 03.03.2023
Revised: 30.04.2023

DOI: 10.4213/tmf10489