The Convergence of Zakharov Equations to the Cubic Nonlinear Schr?dinger Equation

  • 張 續寶

Student thesis: Master's Thesis

Abstract

In this thesis we elaborate on Schochet and Weinstein’s work “The Nonlinear Schr?dinger Limit of Zakharov Equations Governing Langmuir Turbulence” to study the convergence of Zakharov equations to the cubic nonlinear Schr?dinger equation We oberve that the Zakharov equations reduce formally to the cubic nonlinear Schr?dinger equation as the parameter proportional to the ion acoustic speed approaches to infinite Therefore we expect that it should be more and more similar that the behavior of the solutions of the Zakharov equations and the cubic nonlinear Schr?dinger equation with the increase of the parameter in the Zakharov equations To present a justification of this expectation we show that for suitable initial data solutions of Zakharov equations exist and converge to a solution of the cubic nonlinear Schr?dinger equation as the parameter approaches to infinity On the whole we fill up the details skipped in the discussion of Schochet and Weinstein’s work and correct some minor mistakes such as typos in their paper
Date of Award2017 Jul 27
Original languageEnglish
SupervisorYung-Fu Fang (Supervisor)

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