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dc.contributor.advisorNovikov, Sergei Pen_US
dc.contributor.advisorRamachandran, Niranjanen_US
dc.contributor.authorKaipa, Krishna Vinoden_US
dc.date.accessioned2009-10-06T05:37:45Z
dc.date.available2009-10-06T05:37:45Z
dc.date.issued2009en_US
dc.identifier.urihttp://hdl.handle.net/1903/9466
dc.description.abstractThe most basic characteristic of x-quasiperiodic solutions u(x, t) of the sine-Gordon equation u_{tt} -u_{xx} + sin u = 0 is the topological charge density. The real finite-gap solutions u(x, t) are expressed in terms of the Riemann theta-functions of a non-singular hyperelliptic curve, $Gamma$ and a positive generic divisor D of degree g on $Gamma$ , where the spectral data ($Gamma$ ,D) must satisfy some reality conditions. The problem addressed in this dissertation is: to calculate the topological charge density from the theta-functional expressions for the solution u(x, t). This problem has remained unsolved since it was first raised by S.P. Novikov in 1982. The problem is solved here by introducing a new limit of real finite-gap sine-Gordon solutions, which we call the multiscale or elliptic limit. We deform the spectral curve to a singular nodal curve, having elliptic curves as components, for which the calculation of topological charges reduces to two special easier cases.en_US
dc.format.extent341064 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.titleTOPOLOGICAL CHARGE OF REAL FINITE-GAP SINE-GORDON SOLUTIONSen_US
dc.typeDissertationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledFinite-Gapen_US
dc.subject.pquncontrolledSine-Gordonen_US
dc.subject.pquncontrolledTheta functionsen_US
dc.subject.pquncontrolledTopological Chargeen_US


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