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dc.contributor.advisorJakobsen, Per
dc.contributor.authorRørnes, Bjarne
dc.date.accessioned2018-08-16T08:59:44Z
dc.date.available2018-08-16T08:59:44Z
dc.date.issued2018-06-01
dc.description.abstractUltrafast laser pulse experiments and applications are entering a phase that challenges the validity of mathematical models utilised to model longer pulses in nonlinear optics. This thesis aims to propose a possible mathematical model for high intensity laser pulse propagation in air through a multiple scales expansion of Maxwell’s equations and discuss a method on how to solve the corresponding differential equation, known as the modified Korteweg-de Vries equation in to the small dispersion regime. This equation is solvable using a technique named the scattering transform and due to weak dispersion the equation can be solved asymptotically. The method is based on using the asymptotic WKB approximation for the forward scattering problem and reformulating the inverse scattering as a Riemann-Hilbert problem. Both analytical steps and numerical procedures needed to use the method is discussed and implemented. A full example calculation using a particular initial condition is performed and some challenges using the method for more general initial conditions are discussed.en_US
dc.identifier.urihttps://hdl.handle.net/10037/13417
dc.language.isoengen_US
dc.publisherUiT Norges arktiske universiteten_US
dc.publisherUiT The Arctic University of Norwayen_US
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2018 The Author(s)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/3.0en_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)en_US
dc.subject.courseIDMAT-3941
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Applied mathematics: 413en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Anvendt matematikk: 413en_US
dc.titleModelling high intensity laser pulse propagation in air using the modified Korteweg-de Vries equationen_US
dc.typeMaster thesisen_US
dc.typeMastergradsoppgaveen_US


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Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)