Third Order Semilinear Dispersive Equations Related to Deep Water Waves
نویسندگان
چکیده
ABSTRACT. We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and cannot be solved by the classical energy method. To solve the initial value problem, we make full use of pseudodifferential operators with nonsmooth coefficients.
منابع مشابه
Dispersion Estimates for Third Order Equations in Two Dimensions
Two-dimensional deep water waves and some problems in nonlinear optics can be described by various third order dispersive equations, modifying and generalizing the KdV as well as nonlinear Schrödinger equations. We classify all third order polynomials up to certain transformations and study the pointwise decay for the fundamental solutions, Z
متن کاملMathematical Modelling of Generation and Forward Propagation of Dispersive Waves
The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg de Vries equation for purely uni-directional waves. In this paper we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, t...
متن کاملDerivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation
A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic...
متن کاملDiscontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems
Two-dimensional shallow water systems are frequently used in engineering practice to model environmental flows. The benefit of these systems are that, by integration over the water depth, a two-dimensional system is obtained which approximates the full three-dimensional problem. Nevertheless, for most applications the need to propagate waves over many wavelengths means that the numerical soluti...
متن کاملNumerical Study of Non - linear Dispersive Partial Differential Equations
15 Acknowledgements 17 Introduction 19 1 Dispersive Partial Differential Equations and Integrable Systems 29 1.1 Linear Dispersive Partial Differential Equations . . . . . . . . . . . . 29 1.2 Semilinear Dispersive PDEs . . . . . . . . . . . . . . . . . . . . . . . 32 1.2.1 Equations of NLS Type. . . . . . . . . . . . . . . . . . . . . . 33 1.2.2 Equations of KdV Type. . . . . . . . . . . . . ....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004