Applications of Complex Variables to Spectral Theory and Completely Integrable Partial Differential Equations
We generalize the 1+1 Kaup--Broer system to an integrable 2+1 dimensional system via the dressing method. This allows us to compute N-soliton solutions to this 2+1 dimensional system, and also to the 1+1 Kaup–Broer system. This method also allows the computation of new solutions that generalize the...
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| Format: | Dissertation |
| Sprache: | Englisch |
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ProQuest Dissertations & Theses
01.01.2018
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| ISBN: | 9780355884456, 0355884453 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We generalize the 1+1 Kaup--Broer system to an integrable 2+1 dimensional system via the dressing method. This allows us to compute N-soliton solutions to this 2+1 dimensional system, and also to the 1+1 Kaup–Broer system. This method also allows the computation of new solutions that generalize the N-soliton solutions a natural way. We formulate the inverse spectral problem for Hill's operators with bounded periodic potentials as a Riemann–Hilbert problem, and characterize the space of solutions to this Riemann–Hilbert problem. This gives an alternative proof that such a Hill's operator is determined uniquely by its spectral gaps, a Dirichlet eigenvalue in the closure of each spectral gap, and a signature for each Dirichlet eigenvalue in the interior of a spectral gap. |
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| Bibliographie: | SourceType-Dissertations & Theses-1 ObjectType-Dissertation/Thesis-1 content type line 12 |
| ISBN: | 9780355884456 0355884453 |