Graduation Year
2012
Document Type
Dissertation
Degree
Ph.D.
Degree Granting Department
Mathematics and Statistics
Major Professor
Wen-Xiu Ma
Keywords
Conserved quantity, Hamiltonian structure, Integrable coupling, Matrix loop algebras, Soliton hierarchy, Symmetry
Abstract
An investigation into structures of bi-integrable and tri-integrable couplings is undertaken. Our study is based on semi-direct sums of matrix Lie algebras. By introducing new classes of matrix loop Lie algebras, we form new Lax pairs and generate several new bi-integrable and tri-integrable couplings of soliton hierarchies through zero curvature equations. Moreover, we discuss properties of the resulting bi-integrable couplings, including infinitely many commuting symmetries and conserved densities. Their Hamiltonian structures are furnished by applying the variational identities associated with the presented matrix loop Lie algebras.
The goal of this dissertation is to demonstrate the efficiency of our approach and discover rich structures of bi-integrable and tri-integrable couplings by manipulating matrix Lie algebras.
Scholar Commons Citation
Meng, Jinghan, "Bi-Integrable and Tri-Integrable Couplings and Their Hamiltonian Structures" (2012). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/4371
