A course on nonlinear waves
by Samuel S. Shen
Publisher: Dordrecht ; Kluwer Academic, c1993.
ISBN: 0792322924
DDC: 531.1133
LCC: QA927
Edition: (alk. paper)
Summary:
This volume presents a carefully written introduction to nonlinear
waves in the natural sciences and engineering. It not only contains
many classical results but also includes more recent results, dealing
with topics such as the forced Korteweg-de Vries equation and
material relating to X-ray crystallography. The book contains nine
chapters. Chapter 1 concerns asymptotics and nonlinear ordinary
differential equations. Conservation laws are discussed in Chapter 2,
and Chapter 3 considers water waves. The scattering and inverse
scattering method is described in Chapter 4, which also contains a
full explanation of using the inverse scattering method for finding
1-, 2 - and 3-soliton solutions of the Korteweg-de Vries equation.
Chapter 5 studies the Burgers' equation and Chapter 6 discusses the
forced Korteweg-de Vries equations. Here the emphasis is on
steady-state bifurcations and unsteady-state periodic soliton
generation. The Sine-Gordon and nonlinear Schrodinger equations are
the subject of Chapter 7. The final two chapters consider wave
instability and resonance. Every chapter contains problems and
exercises, together with guidance for their solution. The volume
concludes with some appendices which describe symbolic derivations of
certain results on solitons. Several user-friendly MATHEMATICA
packages are included. The prerequisite for using this book is a
background knowledge of basic physics, linear algebra and
differential equations.
Notes:
Includes bibliographical references (p. 317-322) and index.
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