A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem

Autor:	Wen-Xiu Ma
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	matrix spectral problem Lax pair integrable hierarchy monlinear Schrödinger equations modified Korteweg–de Vries equations Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 6, p 927 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12060927
Popis:	The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, and the corresponding bi-Hamiltonian formulation is established by the so-called trace identity, showing the Liouville integrability of the obtained hierarchy. Two illustrative examples are novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations with four components and two adjustable parameters.
Databáze:	Directory of Open Access Journals
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