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Filtering by: Subject Nonlinear wave equations Remove constraint Subject: Nonlinear wave equations Degree Level Doctoral Remove constraint Degree Level: Doctoral

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  • A nonlinear shallow water wave equation and its classical solutions of the cauchy problem

    Creator:
    Crow, John A.
    Abstract:
    A nonlinear wave equation is developed, modeling the evolution in time of shallow water waves over a variable topography. As the usual assumptions of a perfect fluid and an irrotational flow are not made, the resulting model equation is dissipative due to the presence of a viscous boundary layer at...
    Resource Type:
    Dissertation
    Full Text:
    . Guenther A nonlinear wave equation is developed, modeling the evolution in time of shallow water waves

  • The Variable Speed Wave Equation and Perfectly Matched Layers

    Creator:
    Kim, Dojin
    Abstract:
    A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain. We introduce a new formulation from regularizing the classical Un-Split...
    Resource Type:
    Dissertation
    Full Text:
    Doctor of Philosophy in Mathematics presented on June 4, 2015. Title: The Variable Speed Wave Equation

  • Stochastic analysis of a nonlinear ocean structural system

    Creator:
    Lin, Huan
    Abstract:
    Stochastic analysis procedures have been recently applied to analyze nonlinear dynamical systems. In this study, nonlinear responses, stochastic and/or chaotic, are examined and interpreted from a probabilistic perspective. A multi-point-moored ocean structural system under regular and irregular wave excitations is analytically examined via a generalized stochastic Melnikov function and Markov...
    Resource Type:
    Dissertation
    Full Text:
    the nonlinear governing equation with respect to time. A large number of sample response

  • The Davey-Stewartson equations : a numerical study

    Creator:
    White, Peter W.
    Abstract:
    In 1974 Davey and Stewartson used a multi-scale analysis to derive a coupled system of nonlinear partial differential equations which describes the evolution of a three dimensional wave packet in water of a finite depth. This system of equations is the closest integrable two dimensional analog of the well-known one...
    Resource Type:
    Dissertation

  • Numerical inversion of laplace transforms by the trapezoidal-type methods

    Creator:
    Lin, FuSen F.
    Abstract:
    In this dissertation, we investigate three numerical methods for inverting the Laplace transform. These methods are all based on the trapezoidal-type approximations to the Bromwich integral. The first method is the direct integration method: It is a straightforward application of the trapezoidal rule to the Bromwich integral, followed by convergence...
    Resource Type:
    Dissertation
    Full Text:
    have s= +(_1)/c_1Lak= +R1. Again, we multiply by 22 on both sides of the equation (1.11) and then

  • Fractal solutions to the long wave equations

    Creator:
    Ajiwibowo, Harman
    Abstract:
    The fractal dimension of measured ocean wave profiles is found to be in the range of 1.5-1.8. This non-integer dimension indicates the fractal nature of the waves. Standard formulations to analyze waves are based on a differential approach. Since fractals are non-differentiable, this formulation fails for waves with fractal characteristics....
    Resource Type:
    Dissertation
    Full Text:
    the fractal dimension with the nonlinearity of the waves suggests using a nonlinear wave equation. We

  • Nonlinear internal waves on the continental shelf

    Creator:
    Shroyer, Emily L.
    Abstract:
    The properties and evolution of nonlinear internal waves (NLIWs) depend upon the background conditions within which waves form, propagate, and dissipate. As a result, the NLIW field on the New Jersey shelf displayed dramatic variability during the Shallow Water 2006 experiment. Wave variability was exhibited by 1) amplitudes that ranged...
    Resource Type:
    Dissertation
    Full Text:
    2006 and the Nonlinear Internal Wave Initiative . . . 9 2 A DESCRIPTIVE ANALYSIS OF THE NONLINEAR

  • Construction and numerical simulation of a two-dimensional analogue to the KdV equation

    Creator:
    Black, Wendy
    Abstract:
    Arising from an investigation in Hydrodynamics, the Korteweg-de Vries equation demonstrates existence of nonlinear waves that resume their profile after interaction. In this thesis, the classical equations governing wave motion are the starting point for the development of an analogue of the KdV that describes the evolution of a wave...
    Resource Type:
    Dissertation

  • Application of the generalized Melnikov method to weakly damped parametrically excited cross waves with surface tension

    Creator:
    Fadel, Suzan M.
    Abstract:
    The Wiggins-Holmes extension of the generalized Melnikov method (GMM) is applied to weakly damped parametrically excited cross waves with surface tension in a long rectangular wave channel in order to determine if these cross waves are chaotic. The Lagrangian density function for surface waves with surface tension is simplified by...
    Resource Type:
    Dissertation
    Full Text:
    ) prove that the evolution equation governing the cross waves is nonlinear Schrodinger equation with

  • Irregular points in wavemaker boundary value problem

    Creator:
    Tanaka, Yoshihiro
    Abstract:
    A global solution is presented that accurately accounts for the singular behavior at all irregular points. The linearized boundary value problem in a semi-infinite strip in the physical plane is transformed into a smooth unit disk by two successive conformal mappings. The global solution results from a Fredholm integral equation...
    Resource Type:
    Dissertation
    Full Text:
    behavior of solutions obtained from a Fredholm integral equation to the weakly nonlinear diffraction of