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Lump Solutions And Riemann-Hilbert Approach To Soliton Equations, Sumayah A. Batwa

USF Tampa Graduate Theses and Dissertations

In the first part of this dissertation we introduce two matrix iso-spectral problems, a Kaup-Newell type and a generalization of the Dirac spectral problem, associated with the three-dimensional real Lie algebras sl(2;R) and so(3;R), respectively. Through zero curvature equations, we furnish two soliton hierarchies. Hamiltonian structures for the resulting hierarchies are formulated by adopting

the trace identity. In addition, we prove that each of the soliton hierarchies has a bi-Hamiltonian structure which leads to the integrability in the Liouville sense. The motivation of the first part is to construct soliton hierarchies with infinitely many commuting symmetries and conservation laws.

The …