Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Generalized D-Kaup-Newell Integrable Systems And Their Integrable Couplings And Darboux Transformations, Morgan Ashley Mcanally
Generalized D-Kaup-Newell Integrable Systems And Their Integrable Couplings And Darboux Transformations, Morgan Ashley Mcanally
USF Tampa Graduate Theses and Dissertations
We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries, i.e., they are Liouville integrable.
We use the soliton hierarchies and a non-seimisimple matrix loop Lie algebra in order …
Lump, Complexiton And Algebro-Geometric Solutions To Soliton Equations, Yuan Zhou
Lump, Complexiton And Algebro-Geometric Solutions To Soliton Equations, Yuan Zhou
USF Tampa Graduate Theses and Dissertations
In chapter 2, we study two Kaup-Newell-type matrix spectral problems, derive their soliton hierarchies within the zero curvature formulation, and furnish their bi-Hamiltonian structures by the trace identity to show that they are integrable in the Liouville sense. In chapter 5, we obtain the Riemann theta function representation of solutions for the first hierarchy of generalized Kaup-Newell systems.
In chapter 3, using Hirota bilinear forms, we discuss positive quadratic polynomial solutions to generalized bilinear equations, which generate lump or lump-type solutions to nonlinear evolution equations, and propose an algorithm for computing higher-order lump or lump-type solutions. In chapter 4, we …