Asymptotic analysis of a class of perturbed Korteweg-de Vries initial value problems

Cover of: Asymptotic analysis of a class of perturbed Korteweg-de Vries initial value problems | F. de Kerf

Published by Centrum voor Wiskunde en Informatica in [Amsterdam, the Netherlands] .

Written in English

Read online

Subjects:

  • Initial value problems.,
  • Perturbation (Mathematics),
  • Asymptotic expansions.,
  • Mathematical analysis.

Edition Notes

Book details

StatementF. de Kerf.
SeriesCWI tract -- 50.
The Physical Object
Pagination180 p. ;
Number of Pages180
ID Numbers
Open LibraryOL14388806M
ISBN 109061963516

Download Asymptotic analysis of a class of perturbed Korteweg-de Vries initial value problems

Pseudotransient Continuation for Combustion Simulation with Detailed Reaction Mechanisms Recently Searched. Keyword: Method Of Lines (32)Author: Alwyn Scott. Asymptotic analysis of a class of perturbed Korteweg-de Vries initial value problems: Series: CWI tracts, Author: Kerf, de F.

Publisher: Department of Mathematics and Computer Science; VF-programma Toepassingsgerichte Analyse () () () Date issued: Access: Restricted Access: Language: English: Type: Book: PublisherCited by: 5.

Asymptotic analysis of a class of perturbed Korteweg-de Vries initial value problems: Series: CWI Tracts: Author: F. de Kerf: Date issued: Access: Open Access: Type: Book: Publisher: CWI: Publication: ISBN: Persistent Identifier: urn:NBN:nl:ui Metadata: XML: Source: CWIAuthor: F.

deKerf. The asymptotic behavior of the solution u(x, t) of the Korteweg‐deVries equation ut + uux + uxxx = 0 is investigated for the class of problems where the initial data does not give rise to an.

manner, by considering series expansions of solutions of perturbed mathe-matical programs, and 3. the Puiseux series is the natural mathematical object for studying the asymptotic behaviour of a very large class of perturbed mathematical programming problems. Concerning the first of the above claims it is sufficient to note that in.

These formulae yield the conclusion that the dispersive nature of the linearized Korteweg-de Vries equation (in the case of the Cauchy problem) is preserved asymptotically for some perturbation terms in the case of mixed initial-boundary value problems too, when the small parameter goes to zero taking some explicitly specified discrete values.

We describe a set of initial conditions for which the Cauchy problem for a singularly perturbed Korteweg–de-Vries equation with variable coefficients has an asymptotic two-phase solitonlike. tions, but perturbation theory and asymptotic analysis apply to a broad class of problems. In some cases, we may have an explicit expression for x", such as an integral representation, and want to obtain its behavior in the limit "!0.

Asymptotic solutions The rst goal of perturbation theory is to construct a formal asymptotic solution of. Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain. Mathematical Control & Related Fields,1 (1): doi: /mcrf [14] Piotr Kowalski.

Bing-Yu Zhang, Muhammad Usman, Ivonne Rivas, Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain, Mathematical Control and Related Fields, /mcrf, 1, 1, (), ().

The Korteweg–de Vries equation \[ u_t + uu_x + u_{xxx} = 0\] is a nonlinear partial differential equation arising in the study of a number of different physical systems, e.g., water waves, plasma physics, anharmonic lattices, and elastic rods.

We propose an algorithm for the construction of asymptotic m-phase soliton-type solutions of a singularly perturbed Korteweg–de Vries equation with variable coefficients and establish the accuracy with which the main term asymptotically satisfies the considered equation.

Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals.

Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge of differential s: 3. F. de Kerf, Asymptotic Analysis of a Class of Perturbed Korteweg–de Vries Initial Value Problems, Centrum voor Wiskunde en Informatica, Amsterdam, zbMATH Google Scholar T.

Kato, “On the Korteweg–de Vries equation,” Manuscr. Setting α 2 →0 in recovers the Korteweg–de Vries (KdV) equation of Korteweg and de Vries (). () was first derived in Camassa and Holm () by using asymptotic expansions directly in the Hamiltonian for Euler's equations governing inviscid incompressible flow in the shallow water regime.

It was thereby shown to be bi. These initial value problems, and terminal value problems are singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems.

Since the asymptotic expansion approximation is used and the boundary value problem is converted into initial value problems and terminal value problems, therefore the method is called Asymptotic initial value method (AIVM). In general solving an initial value problem.

the solution of this initial value problem as time tgoes to in nity. For a spe-cial case = 0, we present the asymptotic formula of the solution to the ex-tended modi ed Korteweg-de Vries equation in region P= f(x;t) 2R2j0 Korteweg-de Vries. On the basis of the inverse scattering transformation, the Cauchy problem of the coupled modified Korteweg–de Vries equation is transformed to a 3 × 3 matrix Riemann–Hilbert problem.

Two distinct factorizations of the jump matrix for the Riemann–Hilbert problem and a decomposition of the vector-valued spectral function are deduced.

DeKerf, F. Asymptotic analysis of a class of perturbed Korteweg-de Vries initial value problems. CWI Tract Centre for Mathematics and Computer Science, Stichting Math. Centrum, Amsterdam.

Abstract: We investigate an integrable extended modified Korteweg-de Vries equation on the line with the initial value belonging to the Schwartz space. By performing the nonlinear steepest descent analysis of an associated matrix Riemann--Hilbert problem, we obtain the explicit leading-order asymptotics of the solution of this initial value.

Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain. Mathematical Control & Related Fields,1 (1):. Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations.

Browse. Next. Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations. Jun - 27 Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations. Bertola, A. Minakov, Laguerre polynomials and transitional asymptotics of the modified Korteweg–de Vries equation for step-like initial data, Analysis and Mathematical Physics, /s.

The Korteweg – de Vries (KdV) equation is one of the most studied nonlinear partial differen-tial equations. It can be written as qt +6qqx +qxxx = 0, (1) where x and t represent a scaled spatial and temporal independent variable, respectively, and q(x,t) is the function to be determined.

The KdV equation arises in the study of long waves. Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations.

| No Comments. Free Boundary Problems and Asymptotic Behavior of. Next >> >> Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations.

Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations. fevah 0. Uniform asymptotic expresions for the fundamental matrix of singularly perturbed linear systems and applications.

Pages DrĂgan, V. (et al.) Preview Buy Chap19 € Slow/fast decoupling for linear boundary value problems. Pages O’Malley, Robert E., Jr. Asymptotic Analysis II Book Subtitle Surveys and New Trends.

Shuxia Tang. Department of Mechanical & Aerospace Engineering, University of California, San Diego, La Jolla, CAUSA; and UMR Laboratoire Jacques-Louis Lions, Universi.

Chapter 2 offers an improved, simpler presentation of the linearity principle, showing that the heat equation is a linear equation.; Chapter 4 contains a straightforward derivation of the vibrating membrane, an improvement over previous editions.; Additional simpler exercises now appear throughout the text.; Hints are offered for many of the exercises in which partial differential equations.

Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations rogu Free Boundary Problems and Asymptotic Behavior of - Springer.

The purpose of this paper is to present the recent work of Das et al. Plasma Phys. 72, ()] on the existence and stability of the alternative solitary wave solution of fixed width of the combined MKdV-KdV-ZK (Modified Korteweg-de Vries-Korteweg-de Vries-Zakharov-Kuznetsov) equation for the ion-acoustic wave in a magnetized nonthermal plasma consisting of warm adiabatic ions in a.

Non-generic critical behavior for the Korteweg-de Vries equation in the small dispersion limit Tom Claeys, Universit e Catholique Louvain, Belgium The Korteweg-de Vries equation u t+ 6uu x+ 2u xxx= 0 is a Hamiltonian perturbation of the hyperbolic PDE u t+ 6uu x = 0.

The unperturbed equation has solutions that exist only up to. Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations.

by hujil. Free Boundary Problems and Asymptotic Behavior of - Springer. where ε ∈ (0,1] is the perturbation parameter, 0 problems arise in many areas of mathematical physics and fluid mechanics [1–3].Various properties of periodical in time problems in the absence of boundary layers have been investigated earlier by many.

Asymptotic Behavior and Stability Problems in Ordinary Differential Equations. Next › › Asymptotic Behavior and Stability Problems in Ordinary Differential Equations.

Asymptotic Behavior and Stability Problems in Ordinary Differential Equations. No Comments qivo. Radial Eigenvalue Problems Product Solutions, Modes of Vibration, and the Initial Value Problem Laplace's Equation Inside a Spherical Cavity 8. Nonhomogeneous Problems.

Introduction. Heat Flow with Sources and Nonhomogeneous Boundary Conditions. This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis.

It gives the keys to understand a boundary-layer problem and explains the methods to construct an. Since its first publication, Asymptotic Methods in Analysis has received widespread acclaim for its rigorous and original approach to teaching a difficult subject.

This Dover edition, with corrections by the author, offers students, mathematicians, engineers, and physicists not only an inexpensive, comprehensive guide to asymptotic methods but Reviews: 9. "An exactly solvable model for the interaction of linear waves with Korteweg-de Vries solitons," SIAM J.

Math. Anal. 33, pages[With S. Clarke.] [With S. Clarke.] [ J24 ] "Some remarks on a WKB method for the nonselfadjoint Zakharov-Shabat eigenvalue problem with analytic potentials and fast phase," Physica D / We study the Korteweg-de Vries equation posed on the quarter plane with asymptotically t -periodic boundary data for large t > 0.

We derive an expression for the Dirichlet to Neumann map to all orders in the perturbative expansion of a small ϵ &g. A Numerical Method for Nonlinear Singularly Perturbed Multi.

A parameter robust numerical method for a nonlinear system of. Ivonne Rivas, Muhammad Usman, Bingyu Zhang, Global well-posedness and asymptotic behavior of a class of initial-boundary-value problems of the KdV equation on a finite domain, Mathematical Control and Related Fields, Volume 1, Issue 1: .Variational Asymptotic Method (VAM) is a powerful mathematical approach to simplify the process of finding stationary points for a described functional by taking an advantage of small parameters.

VAM is the synergy of variational principles and asymptotic approaches, variational principles are applied to the defined functional as well as the asymptotes are applied to the same functional.

83070 views Thursday, October 22, 2020