Keister, Adrian Clark2014-03-142014-03-142007-06-26etd-06302007-091322http://hdl.handle.net/10919/28169We clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [sic] effect in fiber optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, then it must lie in a certain region in the complex plane. The second issue has to do with a chirped Manakov system. We show that if a system is chirped too much, the soliton effect disappears. While this has been known for some time experimentally, there has not yet been a theoretical result along these lines for the Manakov system.In CopyrightZakharov-Shabatchirpfiber opticsinverse scattering transformsolitoncoupled nonlinear Schrödinger equationsnonlinear Schrödinger equationManakovDissertationhttp://scholar.lib.vt.edu/theses/available/etd-06302007-091322/