NONLINEAR WAVES

AN INTRODUCTION (V4)

By: POPIVANOV PETAR

Write A Review

Hardcover | 24 September 2010

At a Glance

Hardcover
180 Pages

Dimensions(cm)
22.86 x 15.24 x 1.12

Hardcover

RRP $129.99

$116.99

10%OFF

or 4 interest-free payments of $29.25 with

or

Ships in 15 to 25 business days

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, the authors propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks). The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding d-shocks are also considered. At the end of the book the authors study the interaction of two piecewise smooth waves in the case of two space variables and they verify the appearance of logarithmic singularities. As it concerns numerical methods in the case of periodic waves the authors apply Cellular Neural Network (CNN) approach.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Differential Calculus & Equations

Free Boundary Problems and Regularity Theory - Harvey Drouelle

$162.75

Functional Analysis

Entering Hilbert Space

Paperback

RRP $81.99

$73.99

10%
OFF

$LEC NOTE MATH OLYM : SNR SEC (V1) - XU JIAGU$

LEC NOTE MATH OLYM

SNR SEC (V1)

Paperback

RRP $77.99

$70.75

Lecture Notes On Mathematical Olympiad Courses

For Senior Section - Volume 2

Paperback

RRP $84.99

$76.75

10%
OFF

Mathematical Modelling Techniques

Hardcover

RRP $368.00

$315.99

14%
OFF

Mathematical Modelling Techniques

Paperback

RRP $147.00

$132.75

10%
OFF

Nonlinear Fractional Differential Equations of Variable Order - Mohammed Said Souid

$290.99

Free Boundary Problems Via Da Prato-Grisvard Theory

Paperback

RRP $197.00

$187.75

The Calderon Problem

An Introduction

Paperback

RRP $206.00

$195.75

Multivariable Calculus Set Free : Infinitesimals Ride Again - ?? ???, C. Bryan Dawson

$314.75

Preface	p. v
Compact travelling waves and peakon solutions	p. 1
Introduction and main results	p. 1
Proof of Theorem 1.1	p. 4
Proof of Theorem 1.2	p. 8
Generalization of the results	p. 11
CNN realization	p. 13
Existence and profiles of the travelling waves	p. 19
Introduction	p. 19
Camassa-Holm type equations	p. 19
Generalization of the Burger's equation	p. 22
Two component Camassa-Holm system	p. 26
Travelling wave solutions of special type to third order nonlinear PDE	p. 31
Introduction and main results	p. 31
Proof of Theorems 3.1 and 3.2	p. 38
Elliptic functions and applications	p. 43
CNN realization	p. 60
Cauchy problem for the sin-Gordon equation	p. 64
Stability of periodic travelling wave solutions for KDV type equations	p. 69
Introduction and main results	p. 69
Some results from the theory of elliptic functions	p. 75
Interaction of two peakons satisfying the Camassa-Holm equation	p. 85
Introduction. Construction of two peakon solutions	p. 85
Interaction of two peakons	p. 90
Method of the characteristics applied to the Hunter-Saxton equation	p. 97
Classical solutions of the Cauchy problem	p. 97
Weak solutions of the Hunter-Saxton equation	p. 102
Integrable multicomponent Generalizations of Camassa-Holm equation	p. 111
Peakon solutions of Hunter-Saxton equation	p. 111
Explicit formulas for the peakon-type solutions	p. 119
¿-shocks for quasilinear hyperbolic systems in R²	p. 123
Existence of ¿-shocks	p. 123
Weak continuous solutions for the scalar conservation laws	p. 135
Microlocal approach in studying the propagation of nonlinear waves	p. 149
Propagation of jump discontinuities in $$$	p. 149
Creation of logarithmic singularities in $$$	p. 150
Bibliography	p. 159
Index	p. 167
Table of Contents provided by Ingram. All Rights Reserved.

NONLINEAR WAVES

AN INTRODUCTION (V4)

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Differential Calculus & Equations

Free Boundary Problems and Regularity Theory

Differential Equations

An Elementary Approach

The Secret Life of Equations

The 50 Greatest Equations and How They Work

Recent Progress in Special Functions

Contemporary Mathematics

One-Dimensional Ergodic Schrodinger Operators

II. Specific Classes

One-Dimensional Ergodic Schrodinger Operators

II. Specific Classes

Iterative Methods for Linear and Nonlinear Equations

Frontiers in Applied Mathematics

Functional Analysis

Entering Hilbert Space

LEC NOTE MATH OLYM

SNR SEC (V1)

Lecture Notes On Mathematical Olympiad Courses

For Senior Section - Volume 2

Mathematical Modelling Techniques

Mathematical Modelling Techniques

Nonlinear Fractional Differential Equations of Variable Order

Differential Modules over Differential Rings

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Implicit-Explicit Methods for Evolutionary Partial Differential Equations

Modelling, Analysis, Monitoring, and Control of Distributed Parameter Systems:

The Tubular Reactor Case Study

The Calderon Problem

An Introduction

Free Boundary Problems Via Da Prato-Grisvard Theory

The Calderon Problem

An Introduction

Multivariable Calculus Set Free

Infinitesimals Ride Again

A Course on Function Spaces I

Continuous and Integrable Functions

Differential and Difference Equations with Applications in Queueing Theory

Introduction to Differential Equations

Integral and Integro-Differential Equations

Wavelet-Based Numerical Methods

This product is categorised by