Work

A 4 × 4 Matrix Spectral Problem Involving Four Potentials and Its Combined Integrable Hierarchy

Year: 2025

Type: article

Abstract: This paper introduces a specific matrix spectral problem involving four potentials and derives an associated soliton hierarchy using the zero-curvature formulation. The bi-Hamiltonian formulation is derived via the trace identity, thereby establishing the hierarchy’s Liouville integrability. This is exemplified through two systems: generalized combined NLS-type equations and modified KdV-type equations. Owing to Liouville integrability, each member of the hierarchy admits a bi-Hamiltonian structure and, consequently, possesses infinitely many symmetries and conservation laws.

Source: Axioms

DOI: 10.3390/axioms14080594

Authors: Wen-Xiu Ma, Ya-Dong Zhong

Institutions: Khazar University, Zhejiang Normal University, King Abdulaziz University, University of South Florida, North-West University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China