TITLE:
An Eight Component Integrable Hamiltonian Hierarchy from a Reduced Seventh-Order Matrix Spectral Problem
AUTHORS:
Savitha Muthanna, Wen-Xiu Ma
KEYWORDS:
Matrix Spectral Problem, Zero Curvature Equation, Lax Pair, Integrable Hierarchy, NLS Equations, mKdV Equations, Hamiltonian Structure, Lie Bracke
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.6,
June
21,
2024
ABSTRACT: We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.