PERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATION

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dc.contributor.advisorAlbert, John
dc.contributor.authorAdekoya, Oreoluwa
dc.contributor.committeeMemberCrowther, Kathleen
dc.contributor.committeeMemberGrigo, Alexander
dc.contributor.committeeMemberPetrov, Nikola
dc.contributor.committeeMemberRemling, Christian
dc.date.accessioned2019-05-08T18:24:06Z
dc.date.available2019-05-08T18:24:06Z
dc.date.issued2019-05-10
dc.date.manuscript2019-05-02
dc.description.abstractWe study the existence, uniqueness and stability of solutions to the initial-value problem for the periodic dispersion-managed nonlinear Schr\"{o}dinger (DMNLS) equation, an equation that models the propagation of periodic, nonlinear, quasi-monochromatic electromagnetic pulses in a dispersion-managed fiber. The periodic DMNLS equation we derive is the same as the non-periodic DMNLS equation (\ref{eq:1.2}), except with a subtle difference in the operator $T_{(s)}=T_{D(s)}= e^{-iD(s)\partial_x^2}$. The periodic function $D(s)$ still controls the dispersive properties of the optical fiber. With respect to the Cauchy problem for the periodic DMNLS equation, under certain assumptions on the variable dispersion, we use a Strichartz estimate (Theorem \ref{th:3.2}) on the family of operators $T_{D(s)}$ to prove global well-posedness for initial data in $H^r$ for non negative integer values of $r.$ Lastly, we prove results on the existence and stability of ground state solutions by considering the convergence of minimizing sequences for certain variational problems. In the case $\alpha>0,$ the convergence follows from the Rellich-Kondrachov Theorem; in the case $\alpha=0,$ we use a concentration-compactness argument due to Kunze, but with significant modifications.en_US
dc.identifier.urihttps://hdl.handle.net/11244/319611
dc.languageen_USen_US
dc.subjectDispersion-manageden_US
dc.subjectDispersionen_US
dc.subjectNonlinearen_US
dc.subjectSchrodingeren_US
dc.subjectPeriodic dispersion managed nonlinear schrodinger equationen_US
dc.thesis.degreePh.D.en_US
dc.titlePERIODIC SOLUTIONS OF THE DISPERSION-MANAGED NONLINEAR SCHRODINGER EQUATIONen_US
ou.groupCollege of Arts and Sciences::Department of Mathematicsen_US
shareok.nativefileaccessrestricteden_US
shareok.orcid0000-0001-5653-2397en_US

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